Use the image to answer the question.
An illustration shows a section of a ruler. The following measurements are labeled in inches: start fraction 1 over 4 end fraction, start fraction 1 over 2 end fraction, start fraction 3 over 4 end fraction, 1 inch, and 1 start fraction 1 over 4 end fraction.
A ruler is used to measure objects in inches, part of which is shown in the image. This image only shows the left side of the ruler. What would the next measurement be to the right on the ruler?
(1 point)
Responses
1"
−1/4"
1 1/2"
2 1/4"
The next measurement to the right on the ruler after 1 1/4 inches (1 1/4") would be 1 1/2 inches (1 1/2"), as the ruler increments are typically in fractions of an inch and would continue in a sequence from the values given.
So the correct answer is:
1 1/2"
Use the image to answer the question.
A horizontal rectangle is shown sectioned by a large shaded rectangle in the center bordered by two small vertical rectangles on either end. There are nine evenly-spaced vertical lines descending from the top of the shaded rectangle, forming ten equal spaces. The center line is labeled 50, with the other lines on both sides reading 40, 30, 20 and 10.
A football player runs the ball from the 20-yard line on one side of the field to the 20-yard line on the other side. How many yards did the player run?
(1 point)
yards
According to the description, the shaded rectangle is centered and the individual vertical lines represent 10-yard increments, with the central line labeled as the 50-yard line.
If a football player runs from the 20-yard line on one side to the 20-yard line on the other side, they would have traversed the 30-yard line, the 40-yard line, the 50-yard line, then the opposing 40-yard line, and finally the opposing 30-yard line.
To calculate the total yards run, you can add the individual segments together:
- 20-yard line to the 30-yard line = 10 yards
- 30-yard line to the 40-yard line = 10 yards
- 40-yard line to the 50-yard line = 10 yards
- 50-yard line to the opposing 40-yard line = 10 yards
- Opposing 40-yard line to the opposing 30-yard line = 10 yards
- Opposing 30-yard line to the opposing 20-yard line = 10 yards
Now, sum the distances run in each segment:
10 yards + 10 yards + 10 yards + 10 yards + 10 yards + 10 yards = 60 yards
Therefore, the football player ran a total of 60 yards.
Which two quadrants have negative x-values?(1 point)
Responses
I and IV
I and IV
II and III
II and III
I and II
I and II
III and IV
III and IV
In the Cartesian coordinate system, the quadrants are numbered counterclockwise starting from the upper right quadrant, which is Quadrant I. Here is how the quadrants are labeled, along with the signs of their x and y values:
- Quadrant I (1st Quadrant): x > 0, y > 0
- Quadrant II (2nd Quadrant): x < 0, y > 0
- Quadrant III (3rd Quadrant): x < 0, y < 0
- Quadrant IV (4th Quadrant): x > 0, y < 0
The quadrants with negative x-values are Quadrant II and Quadrant III.
Therefore, the correct response is:
II and III
How many quadrants on a coordinate plane have positive x-values?(1 point)
On a coordinate plane, there are four quadrants. The quadrants with positive x-values are:
- Quadrant I: Both x and y are positive.
- Quadrant IV: x is positive, and y is negative.
So there are 2 quadrants on a coordinate plane with positive x-values.
Use the image to answer the question.
A coordinate plane shows the x-axis and y-axis labeled, both ranging from negative 6 to 6 in increments of 1. Quadrants 1 to 4 are labeled. Quadrant 1 is labeled with left parenthesis positive sign comma positive sign right parenthesis. Quadrant 2 is labeled with left parenthesis negative sign comma positive sign right parenthesis. Quadrant 3 is labeled with left parenthesis negative sign comma negative sign right parenthesis. Quadrant 4 is labeled with left parenthesis positive sign comma negative sign right parenthesis.
What can be the value of x
so that the ordered pair (x, 13) is located in Quadrant II?
(1 point)
Responses
13
13
9
9
0
0
−14
negative 14
In order for the ordered pair (x, 13) to be located in Quadrant II of the coordinate plane, the x-value must be negative, and the y-value must be positive. Since the y-value is already stated as positive 13, we are only focusing on the x-value.
Quadrant II is characterized by negative x-values and positive y-values. Therefore, the x-value must be negative to be in Quadrant II. Among the given choices, the one that is negative is:
−14 (negative 14)
Thus, (x, 13) will be in Quadrant II if x is −14.
Which of the following pairs of points is a reflection of each other across the y
-axis?(1 point)
Responses
(8, 1) and (1, 8)
Left Parenthesis 8 comma 1 Right Parenthesis and Left Parenthesis 1 comma 8 Right Parenthesis
(1, 17) and (1, −17)
Left Parenthesis 1 comma 17 Right Parenthesis and Left Parenthesis 1 comma negative 17 Right Parenthesis
(−6, −10) and (6, 10)
Left Parenthesis negative 6 comma negative 10 Right Parenthesis and Left Parenthesis 6 comma 10 Right Parenthesis
(13, −11) and (−13, −11)
A reflection across the y-axis means that the x-values of the pair of points will be equal in magnitude but opposite in sign, while the y-values will remain the same.
Comparing the given pairs of points:
- (8, 1) and (1, 8): The x and y values are swapped, not reflected across the y-axis.
- (1, 17) and (1, −17): The y-values are opposite in sign, but for a reflection across the y-axis, the y-values should stay the same.
- (−6, −10) and (6, 10): The x-values are opposite in sign, which is correct, but the y-values have also changed signs. This is more of a reflection across the origin, not just the y-axis.
- (13, −11) and (−13, −11): The x-values are opposite in sign and the y-values are the same, which is the correct condition for a reflection across the y-axis.
Therefore, the correct pair of points that is a reflection of each other across the y-axis is:
(13, −11) and (−13, −11)
Use the image to answer the question.
A coordinate plane shows the x- and y- axes ranging from negative 16 to 16 in increments of 2. The point left parenthesis 14 comma negative 15 right parenthesis is plotted on the plane.
The point (14, −15) is reflected across both the x- and y-axes. What are the coordinates of the reflected point?
(1 point)
(
,
)
To reflect the point (14, −15) across both the x- and y-axes, you need to change the sign of both the x-coordinate and the y-coordinate.
The x-coordinate is positive 14, reflecting it across the y-axis will make it negative. The y-coordinate is negative 15, reflecting it across the x-axis will make it positive. Thus, the reflected point will have the coordinates:
(-14, 15)
The coordinates of the reflected point are:
(-14, 15)
Use the image to answer the question.
A coordinate plane has an x-axis and y-axis both ranging from negative 7 to 7 in increments of 1. Points labeled with zoo animal names are plotted. Quadrant 1 is labeled with left parenthesis positive sign comma positive sign right parenthesis. Pandas and koalas are plotted in quadrant 1. Pandas is shown at 2 increments on the x-axis and 3 increments on the y-axis. Koalas is shown at 5 increments on the x-axis and 2 increments on the y-axis. Quadrant 2 is labeled with left parenthesis negative sign comma positive sign right parenthesis. Giraffes, lions, and rhinos are plotted in quadrant 2. Giraffes is shown at 5 increments on the x-axis and 2 increments on the y-axis. Lions is shown at 3 increments on the x-asix and 5 increments on the y-axis. Rhinos is shown at 1 increment on the x-axis and 1 increment on the y-axis. Quadrant 3 is labeled with left parenthesis negative sign comma negative sign right parenthesis. Apes and chimpanzees are plotted in Quadrant 3. Apes is shown at 5 increments on the x-axis and 2 increments on the y-axis. Chimpanzees is shown at 7 increments on the x-axis and 5 increments on the y-axis. Quadrant 4 is labeled with left parenthesis positive sign comma negative sign right parenthesis. Frogs, lizards, and snakes are plotted in quadrant 4. Frogs is shown at 1 increment on the x-axis and 4 increments on the y-axis. Lizards is shown at 1 increment on the x-axis and 6 increments on the y-axis. Snakes is shown at 6 increments on the x-axis and 2 increments on the y-axis.
Sana is at the zoo and wants to see the frogs. Where should she go?
(1 point)
Responses
(1, 4)
left parenthesis 1 comma 4 right parenthesis
(1, −4)
left parenthesis 1 comma negative 4 right parenthesis
(4, 1)
left parenthesis 4 comma 1 right parenthesis
(−4, 1)
According to the information provided in the description of the image, the "Frogs" are plotted in Quadrant 4 of the coordinate plane. Quadrant 4 is labeled with the signs (positive, negative), meaning the x-coordinates are positive and the y-coordinates are negative in this quadrant.
"Frogs" is shown at 1 increment on the x-axis and 4 increments on the y-axis in Quadrant 4. Since the increments on the y-axis are negative in Quadrant 4, "Frogs" would be located at the coordinates:
(1, −4)
So, if Sana wants to see the frogs at the zoo, she should go to the location with the coordinates:
(1, −4)
left parenthesis 1 comma negative 4 right parenthesis
Use the image to answer the question.
A coordinate plane has an x-axis and y-axis both ranging from negative 7 to 7 in increments of 1. Points labeled with zoo animal names are plotted. Quadrant 1 is labeled with left parenthesis positive sign comma positive sign right parenthesis. Pandas and koalas are plotted in quadrant 1. Pandas is shown at 2 increments on the x-axis and 3 increments on the y-axis. Koalas is shown at 5 increments on the x-axis and 2 increments on the y-axis. Quadrant 2 is labeled with left parenthesis negative sign comma positive sign right parenthesis. Giraffes, lions, and rhinos are plotted in quadrant 2. Giraffes is shown at 5 increments on the x-axis and 2 increments on the y-axis. Lions is shown at 3 increments on the x-asix and 5 increments on the y-axis. Rhinos is shown at 1 increment on the x-axis and 1 increment on the y-axis. Quadrant 3 is labeled with left parenthesis negative sign comma negative sign right parenthesis. Apes and chimpanzees are plotted in Quadrant 3. Apes is shown at 5 increments on the x-axis and 2 increments on the y-axis. Chimpanzees is shown at 7 increments on the x-axis and 5 increments on the y-axis. Quadrant 4 is labeled with left parenthesis positive sign comma negative sign right parenthesis. Frogs, lizards, and snakes are plotted in quadrant 4. Frogs is shown at 1 increment on the x-axis and 4 increments on the y-axis. Lizards is shown at 1 increment on the x-axis and 6 increments on the y-axis. Snakes is shown at 6 increments on the x-axis and 2 increments on the y-axis.
Sana is at the zoo and ends up at (−5, 2). What animal does she find there?
(1 point)
Responses
lizards
lizards
apes
apes
giraffes
giraffes
frogs
Given the coordinates (−5, 2), we look at the labeled points in the description of the image.
The negative in the x-coordinate places the point in the left half of the coordinate plane, which includes Quadrants II and III, which have negative x-values, while the positive y-coordinate narrows it down to Quadrant II because this quadrant is characterized by negative x-values and positive y-values.
The point (-5, 2) is indicated as having 5 increments on the x-axis (negative side) and 2 increments on the y-axis (positive side). According to the description, the "Giraffes" are plotted in Quadrant 2 at 5 increments on the x-axis and 2 increments on the y-axis.
Therefore, Sana finds herself at the location of the "Giraffes" which are at the coordinates (−5, 2).
The correct response is:
giraffes
giraffes
Use the image to answer the question.
A coordinate grid shows the x-axis ranging from negative 12 to 12 and the y-axis also ranging from negative 12 to 12. Points labeled with winter activities are plotted. Sledding is plotted at left parenthesis 2 comma 12 right parenthesis. Skiing is plotted at left parenthesis negative 8 comma negative 4 right parenthesis, and ice skating is plotted at left parenthesis 2 comma negative 4 right parenthesis.
Shahriyar is at a winter park with his family. They go sledding first, then ice skating, then skiing. What is the total distance traveled between these locations?
(1 point)
$$
Skip to navigation
A graph plots cups of yogurt versus slices of mango on x and y axes, respectively, with the x-axis ranging from 0 to 10 in increments of 1 and the y-axis ranging from 0 to 80 in increments of 8. Details of the plots are as follows: left parenthesis 2 comma 16 right parenthesis; left parenthesis 4 comma 32 right parenthesis; and left parenthesis 6 comma 48 right parenthesis.
A graph with the x-axis representing scoops of red paint ranging from 0 to 12 in increments of 1 and the y-axis representing scoops of yellow paint ranging from 0 to 30 in increments of 1 shows seven plotted points, 5 for option A and 2 option B. Option A has the following points: left parenthesis 2 comma 5 right parenthesis; left parenthesis 4 comma 10 right parenthesis; left parenthesis 6 comma 15 right parenthesis; left parenthesis 8 comma 20 right parenthesis; and left parenthesis 10 comma 25 right parenthesis. Option B has the following points: left parenthesis 5 comma 11 right parenthesis and left parenthesis 10 comma 22 right parenthesis.
A coordinate plane has an x-axis and y-axis both ranging from negative 7 to 7 in increments of 1. Labeled points A, B, D, F, G, I, L, M, O, S, T and W are plotted. Quadrant 1 is labeled with left parenthesis positive sign comma positive sign right parenthesis. Labeled point F is plotted in quadrant 1. Point F is shown at 2 increments on the x-axis and 3 increments on the y-axis. Quadrant 2 is labeled with left parenthesis negative sign comma positive sign right parenthesis. Labeled points A, B, D, G, and I are plotted in quadrant 2. Point A is shown at 4 increments on the x-axis and 3 increments on the y-axis. Point B is shown at 5 increments on the x-asix and 6 increments on the y-axis. Point D is shown at 7 increments on the x-axis and 1 increment on the y-axis. Point G is shown at 3 increments on the x-axis and 3 increments on the y-axis. Point I is shown at 5 increments on the x-axis and 1 increment on the y-axis. Quadrant 3 is labeled with left parenthesis negative sign comma negative sign right parenthesis. Labeled points L, M, and S are plotted in Quadrant 3. Point L is shown at 2 increments on the x-axis and 2 increments on the y-axis. Point M is shown at 6 increments on the x-axis and 4 increments on the y-axis. Point S is shown at 2 increments on the x-axis and 7 increments on the y-axis. Quadrant 4 is labeled with left parenthesis positive sign comma negative sign right parenthesis. Labeled points O, T, and W are plotted in quadrant 4. Point O is shown at 3 increments on the x-axis and 3 increments on the y-axis. Point T is shown at 2 increments on the x-axis and 5 increments on the y-axis. Point W is shown at 6 increments on the x-axis and 6 increments on the y-axis.
Use the image to answer the question.
A coordinate grid shows the x-axis ranging from negative 12 to 12 and the y-axis also ranging from negative 12 to 12. Points labeled with winter activities are plotted. Sledding is plotted at left parenthesis 2 comma 12 right parenthesis. Skiing is plotted at left parenthesis negative 8 comma negative 4 right parenthesis, and ice skating is plotted at left parenthesis 2 comma negative 4 right parenthesis.
Shahriyar is at a winter park with his family. They go sledding first, then ice skating, then skiing. What is the total distance traveled between these locations?
(1 point)
$$
To calculate the total distance traveled between these locations on the coordinate grid, we will determine the distance between each pair of consecutive activities and then sum those distances.
The points are given as follows:
- Sledding: (2, 12)
- Ice Skating: (2, -4)
- Skiing: (-8, -4)
First, we need to find the distance between Sledding and Ice Skating. Since they have the same x-coordinate value, the distance between them will be the difference in y-coordinates.
Distance between Sledding and Ice Skating:
= |12 - (-4)| = |12 + 4| = 16
Next, we find the distance between Ice Skating and Skiing. We'll use the distance formula for two points in the coordinate plane, which is:
\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
So for Ice Skating (2, -4) and Skiing (-8, -4), we have:
Distance between Ice Skating and Skiing:
= √[(-8 - 2)^2 + (-4 - (-4))^2]
= √[(-10)^2 + (0)^2]
= √(100 + 0)
= 10
Now, we add the two distances:
Total distance traveled = Distance between Sledding and Ice Skating + Distance between Ice Skating and Skiing
= 16 + 10
= 26
Therefore, the total distance traveled between these locations is 26 units.
Which of the following points has a distance of 3 from the point (−7, 4)?(1 point)
Responses
(−7, −1)
Left Parenthesis negative 7 comma negative 1 Right Parenthesis
(−10, 4)
Left Parenthesis negative 10 comma 4 Right Parenthesis
(4, 4)
Left Parenthesis 4 comma 4 Right Parenthesis
(10, 4)
To determine which of the following points has a distance of 3 from the point (−7, 4), we need to consider the distance formula in a coordinate plane:
\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, we want the distance to be 3, and our starting point is (−7, 4). We can quickly test each answer choice to see which point would result in a distance of 3.
- (−7, −1): The difference in the x-coordinates is 0, and the difference in the y-coordinates is 4 - (-1) = 5. This would not correspond to a distance of 3.
- (−10, 4): The difference in the x-coordinates is −10 - (−7) = −3, and the difference in y-coordinates is 0. The distance is precisely 3, which can also be confirmed by applying the distance formula: \( \sqrt{(-3)^2 + (0)^2} = \sqrt{9 + 0} = 3 \).
- (4, 4): The difference in the x-coordinates is 4 - (−7) = 11, which is already larger than the desired distance of 3 without considering y-coordinates.
- (10, 4): Similar to the previous point, the difference in the x-coordinates is too large.
Therefore, the point with a distance of 3 from the point (−7, 4) is:
(−10, 4)
Left Parenthesis negative 10 comma 4 Right Parenthesis
Use the image to answer the question.
A graph plots cups of yogurt versus slices of mango on x and y axes, respectively, with the x-axis ranging from 0 to 10 in increments of 1 and the y-axis ranging from 0 to 80 in increments of 8. Details of the plots are as follows: left parenthesis 2 comma 16 right parenthesis; left parenthesis 4 comma 32 right parenthesis; and left parenthesis 6 comma 48 right parenthesis.
How many slices of mango are needed for 10 cups of yogurt?
(1 point)
slices of mango
The graph described shows a linear relationship between cups of yogurt and slices of mango. Since the x-axis represents cups of yogurt and the y-axis represents slices of mango, we can look at the given points to determine the rate at which slices of mango increase with each cup of yogurt.
From the points given:
- (2, 16) means that for 2 cups of yogurt, 16 slices of mango are needed.
- (4, 32) means that for 4 cups of yogurt, 32 slices of mango are needed.
- (6, 48) means that for 6 cups of yogurt, 48 slices of mango are needed.
We can see that the number of slices of mango is increasing by a multiple of 8 for each cup of yogurt. In other words, each cup of yogurt requires 8 slices of mango (16 slices for 2 cups, 32 slices for 4 cups, etc.).
To figure out how many slices of mango are needed for 10 cups of yogurt, we just need to continue this pattern:
10 cups of yogurt x 8 slices of mango per cup = 80 slices of mango
So, for 10 cups of yogurt, you would need 80 slices of mango.
Use the image to answer the question.
A graph with the x-axis representing scoops of red paint ranging from 0 to 12 in increments of 1 and the y-axis representing scoops of yellow paint ranging from 0 to 30 in increments of 1 shows seven plotted points, 5 for option A and 2 option B. Option A has the following points: left parenthesis 2 comma 5 right parenthesis; left parenthesis 4 comma 10 right parenthesis; left parenthesis 6 comma 15 right parenthesis; left parenthesis 8 comma 20 right parenthesis; and left parenthesis 10 comma 25 right parenthesis. Option B has the following points: left parenthesis 5 comma 11 right parenthesis and left parenthesis 10 comma 22 right parenthesis.
Which coordinate pair should be plotted next for Option B to keep the ratio the same?
(1 point)
Responses
(15, 23)
left parenthesis 15 comma 23 right parenthesis
(11, 33)
left parenthesis 11 comma 33 right parenthesis
(15, 33)
left parenthesis 15 comma 33 right parenthesis
(11, 23)
left parenthesis 11 comma 23 right parenthesis
Skip to navigation
A coordinate plane has an x-axis and y-axis both ranging from negative 7 to 7 in increments of 1. Labeled points A, B, D, F, G, I, L, M, O, S, T and W are plotted. Quadrant 1 is labeled with left parenthesis positive sign comma positive sign right parenthesis. Labeled point F is plotted in quadrant 1. Point F is shown at 2 increments on the x-axis and 3 increments on the y-axis. Quadrant 2 is labeled with left parenthesis negative sign comma positive sign right parenthesis. Labeled points A, B, D, G, and I are plotted in quadrant 2. Point A is shown at 4 increments on the x-axis and 3 increments on the y-axis. Point B is shown at 5 increments on the x-asix and 6 increments on the y-axis. Point D is shown at 7 increments on the x-axis and 1 increment on the y-axis. Point G is shown at 3 increments on the x-axis and 3 increments on the y-axis. Point I is shown at 5 increments on the x-axis and 1 increment on the y-axis. Quadrant 3 is labeled with left parenthesis negative sign comma negative sign right parenthesis. Labeled points L, M, and S are plotted in Quadrant 3. Point L is shown at 2 increments on the x-axis and 2 increments on the y-axis. Point M is shown at 6 increments on the x-axis and 4 increments on the y-axis. Point S is shown at 2 increments on the x-axis and 7 increments on the y-axis. Quadrant 4 is labeled with left parenthesis positive sign comma negative sign right parenthesis. Labeled points O, T, and W are plotted in quadrant 4. Point O is shown at 3 increments on the x-axis and 3 increments on the y-axis. Point T is shown at 2 increments on the x-axis and 5 increments on the y-axis. Point W is shown at 6 increments on the x-axis and 6 increments on the y-axis.
Use the image to answer the question.
A graph with the x-axis representing scoops of red paint ranging from 0 to 12 in increments of 1 and the y-axis representing scoops of yellow paint ranging from 0 to 30 in increments of 1 shows seven plotted points, 5 for option A and 2 option B. Option A has the following points: left parenthesis 2 comma 5 right parenthesis; left parenthesis 4 comma 10 right parenthesis; left parenthesis 6 comma 15 right parenthesis; left parenthesis 8 comma 20 right parenthesis; and left parenthesis 10 comma 25 right parenthesis. Option B has the following points: left parenthesis 5 comma 11 right parenthesis and left parenthesis 10 comma 22 right parenthesis.
Which coordinate pair should be plotted next for Option B to keep the ratio the same?
(1 point)
Responses
(15, 23)
left parenthesis 15 comma 23 right parenthesis
(11, 33)
left parenthesis 11 comma 33 right parenthesis
(15, 33)
left parenthesis 15 comma 33 right parenthesis
(11, 23)
To determine which coordinate pair should be plotted next for Option B while keeping the ratio the same, we first need to identify the ratio of scoops of yellow paint to scoops of red paint for Option B.
Given points for Option B:
- (5, 11)
- (10, 22)
We divide the number of scoops of yellow paint by the number of scoops of red paint to find the ratio:
For the point (5, 11):
11 / 5 = 2.2
For the point (10, 22):
22 / 10 = 2.2
We can see that the ratio of yellow to red paint for Option B is consistent at 2.2.
Now let's evaluate the given options:
A. (15, 23):
The ratio would be 23 / 15, which is not equal to 2.2.
B. (11, 33):
The ratio would be 33 / 11, which simplifies to 3, and that is not equal to 2.2.
C. (15, 33):
The ratio would be 33 / 15, which is also not equal to 2.2.
D. (11, 23):
The ratio would be 23 / 11, which simplifies to approximately 2.09, and that is not equal to 2.2.
None of the given options exactly match the ratio of 2.2. However, if we were to extend the ratio for the next likely integer value of scoops of red paint (considering the increments) which would be 15, then:
15 scoops of red paint x 2.2 = 33 scoops of yellow paint
The closest match to a correct and consistent ratio based on the information provided is:
(15, 33)
left parenthesis 15 comma 33 right parenthesis
Option C seems to have a typo as the ratio is correct, but the given coordinate is not consistent with the previous increments. The next logical point based on the pattern would actually be (15, 33) based on the ratio. There may be an error in the provided response options, as none of them have the exact correct ratio, but C is the closest despite the unintended inconsistency.
Use the image to answer the question.
A coordinate plane has an x-axis and y-axis both ranging from negative 7 to 7 in increments of 1. Labeled points A, B, D, F, G, I, L, M, O, S, T and W are plotted. Quadrant 1 is labeled with left parenthesis positive sign comma positive sign right parenthesis. Labeled point F is plotted in quadrant 1. Point F is shown at 2 increments on the x-axis and 3 increments on the y-axis. Quadrant 2 is labeled with left parenthesis negative sign comma positive sign right parenthesis. Labeled points A, B, D, G, and I are plotted in quadrant 2. Point A is shown at 4 increments on the x-axis and 3 increments on the y-axis. Point B is shown at 5 increments on the x-asix and 6 increments on the y-axis. Point D is shown at 7 increments on the x-axis and 1 increment on the y-axis. Point G is shown at 3 increments on the x-axis and 3 increments on the y-axis. Point I is shown at 5 increments on the x-axis and 1 increment on the y-axis. Quadrant 3 is labeled with left parenthesis negative sign comma negative sign right parenthesis. Labeled points L, M, and S are plotted in Quadrant 3. Point L is shown at 2 increments on the x-axis and 2 increments on the y-axis. Point M is shown at 6 increments on the x-axis and 4 increments on the y-axis. Point S is shown at 2 increments on the x-axis and 7 increments on the y-axis. Quadrant 4 is labeled with left parenthesis positive sign comma negative sign right parenthesis. Labeled points O, T, and W are plotted in quadrant 4. Point O is shown at 3 increments on the x-axis and 3 increments on the y-axis. Point T is shown at 2 increments on the x-axis and 5 increments on the y-axis. Point W is shown at 6 increments on the x-axis and 6 increments on the y-axis.
Marcelle uses the coordinate graph shown to make words. He makes the word FIST.
a. What are the coordinates of each of the letters in the word FIST?
b. Change the first letter of the word FIST with another letter in the graph to make another word. What is your word?
c. What are the coordinates of the new letter?
d. How do the coordinates of the new letter compare to the coordinates of F?
a. The coordinates of each of the letters in the word FIST, based on the information provided are:
- F: (2, 3) [Quadrant 1]
- I: (5, 1) [Quadrant 2]
- S: (2, -7) [Quadrant 3]
- T: (2, -5) [Quadrant 4]
b. To change the first letter of the word FIST to make another word, we will use the list of available letters from the graph. Possible replacements for the letter F could be A, B, D, G, L, M, O, or W. Since we need to form a real word and given the constraints of the letters I, S, and T, the replacement could be the letter M to make the word "MIST".
c. The coordinates of the new letter M are:
- M: (6, -4) [Quadrant 3]
d. How the coordinates of the letter M compare to the coordinates of F:
- The original letter F has coordinates (2, 3), which are in Quadrant 1.
- The new letter M has coordinates (6, -4), which are in Quadrant 3.
The comparison reveals that while F is located in the positive-positive quadrant (Quadrant 1), M is located in the negative-positive quadrant (Quadrant 3) which indicates that their x-coordinates have the same sign but are different in magnitude, and their y-coordinates are of the opposite sign with different magnitudes.