Gina plotted the points (−3, 4), (4, 4), (−3, −2), and (4, −2)
on the coordinate plane.
A graph is shown in the xy-plane. The values on the x-axis ranges from negative 8 to 8 in increments of 2 and the values on the y-axis ranges from negative 8 to 8 in increments of 2. Four points are marked on the graph whose coordinates are (negative 3, 4), (4, 4), (negative 3, negative 2), and (4, negative 2).
A. Determine the height of the quadrilateral.
B. Determine the length of the quadrilateral.
C. Gina said the points formed a square. Is she correct? Explain your reasoning.
A. To determine the height of the quadrilateral, we look at the difference in the y-coordinates of the points. Since two points have a y-coordinate of 4 and the other two have a y-coordinate of -2, the height is 4 - (-2) = 6 units.
B. To determine the length of the quadrilateral, we look at the difference in the x-coordinates of the points. Since two points have an x-coordinate of -3 and the other two have an x-coordinate of 4, the length is 4 - (-3) = 7 units.
C. For the points to form a square, the length and height should be equal. Since the length is 7 and the height is 6, they are not equal, so Gina is not correct. The points do not form a square. The quadrilateral is a rectangle, because it has four 90-degree angles and opposite sides are equal in length.
Is that the right explanation Bot?
Yes, that is the correct explanation.
Can somebody help me with a question that i have?
Of course! What is your question?
Consider points A to F shown on the coordinate plane.
A graph is shown in the xy-plane. The values on the x-axis ranges from negative 8 to 8 in increments of 2 and the values on the y-axis ranges from negative 8 to 8 in increments of 2. Six points, Upper A, Upper B, Upper C, Upper D, Upper E, and Upper F are marked on the graph. The point Upper A is 4 units above the x-axis and 6 units to the left of the y-axis, the point Upper B is 3 units above the x-axis and 5 units to the right of the y-axis, the point Upper C is 7 units below the x-axis and 5 units to the left of the y-axis, the point Upper D is 2 units below the x-axis and 8 units to the right of the y-axis, the point Upper E is on the x-axis and 7 units to the left of the y-axis, and the point Upper F is on the y-axis and 6 units above the x-axis.
What are the coordinates of points C, D, and E?
The coordinates of point C are (-5,-7) because it is 5 units to the left of the y-axis and 7 units below the x-axis.
The coordinates of point D are (8,-2) because it is 8 units to the right of the y-axis and 2 units below the x-axis.
The coordinates of point E are (-7,0) because it is 7 units to the left of the y-axis and on the x-axis (where y-coordinate is 0).
For the coordinates of C, does the -7 go before the -5?
No, the x-coordinate always comes before the y-coordinate. So for the coordinates of point C, it is (-5,-7) and not (-7,-5).
Ok, thank you. I also have another question that is difficult
On the coordinate plane shown, points A
(
−
5
,
−
6
)
, B
(
2
,
−
6
)
, C
(
8
,
5
)
, and D
(
−
7
,
5
)
are plotted and connected with line segments to form a trapezoid.
A graph is shown in the xy-plane. The values on the x-axis ranges from negative 8 to 8 in increments of 2 and the values on the y-axis ranges from negative 8 to 8 in increments of 2. Four points Upper A, Upper B, Upper C, and Upper D are marked on the graph with coordinates (negative 5, negative 6), (2, negative 6), (8, 5), and (negative 7, 5) respectively. The four points are joined together to form a trapezium UpperWord ABCD.
What is the height of the trapezoid?
To find the height of the trapezoid, we need to find the perpendicular distance between the parallel sides, which in this case are sides AB and CD.
The length of AB is 2 - (-5) = 7 units, and the length of CD is 8 - (-7) = 15 units.
Since ADBC is a trapezoid, the height forms a right-angle triangle with sides of length 7, 15 and the height.
Using the Pythagorean theorem, we can find the height:
height^2 = 15^2 - 7^2
height^2 = 225 - 49
height^2 = 176
height = sqrt(176)
height = 4sqrt(11)
Therefore, the height of the trapezoid is 4sqrt(11) units.
Can the answer be a tad bit more simpler?
Sure! We can simplify the answer by using a calculator to approximate the value of the square root of 176.
height ≈ 13.29
So the height of the trapezoid is approximately 13.29 units.
Which coordinate pairs lie on the x-axis? Select two answers.
A.
(
0
,
5
)
B.
(
0
,
−
13
)
C.
(
4
,
0
)
D.
(
−
1
,
0
)
The coordinate pairs that lie on the x-axis have a y-coordinate of 0. So, the correct answer would be:
D. (−1, 0) and C. (4, 0)
Thus, (−1,0) and (4,0) lie on the x-axis.
Thank you, Bot!
You're welcome! If you have any more questions, feel free to ask.
Which situation could best be represented by the graph?
A graph is shown whose horizontal axis is labeled as Distance and the vertical axis is labeled as Time. A line starts from a point on the vertical axis above the origin, goes down, intersects the horizontal axis and enters the fourth quadrant. It then becomes parallel to the horizontal axis for some time then goes up and ends at a point on the horizontal axis.
A.
Felicia swam across the surface of the pool.
B.
George dove underwater and came right back up.
C.
Laura jumped off the diving board and swam along the bottom before surfacing.
D.
Carl climbed up the diving board, changed his mind, and climbed back down.
The situation that could best be represented by the graph is:
C. Laura jumped off the diving board and swam along the bottom before surfacing.
The line starts from a point on the vertical axis above the origin, representing Laura jumping off the diving board, then goes down, intersecting the horizontal axis, representing Laura sinking to the bottom, before entering the fourth quadrant, representing her swimming along the bottom. Then, the line becomes parallel to the horizontal axis for some time, representing Laura swimming at a constant speed, before going up and ending at a point on the horizontal axis, representing Laura surfacing.
Brett opened a checking account. The graphs show how the balance changed over time.
Match each description with the appropriate graph.
Brett had an overdraft for several weeks. Then, he deposited just enough money to eliminate the overdraft.Brett deposited money into his account and then, did nothing.Brett withdrew money regularly until he had a large overdraft. Then, he deposited more money.
The horizontal axis is labeled as Time and the vertical axis is labeled as Account balance. In Graph 1, a line starts from a point on the vertical axis, first goes down, intersects the horizontal axis, enters the fourth quadrant, then goes up, again intersects the horizontal axis and enters the first quadrant again.
double side arrow
The horizontal axis is labeled as Time and the vertical axis is labeled as Account balance. In Graph 2, a line starts from a point on the vertical axis below the origin, moves parallel to the horizontal axis then goes up straight and moves parallel to the vertical axis then finally moves along the horizontal axis.
double side arrow
The horizontal axis is labeled as Time and the vertical axis is labeled as Account balance. In Graph 3, a line starts from the origin, first goes up to a point then moves parallel to the horizontal axis.
Brett had an overdraft for several weeks. Then, he deposited just enough money to eliminate the overdraft. --> Graph 1
Brett deposited money into his account and then, did nothing. --> Graph 2
Brett withdrew money regularly until he had a large overdraft. Then, he deposited more money. --> Graph 3
On the coordinate plane shown, the points A(4, 4),
B
(
−
2
,
4
)
, and
C
(
−
2
,
−
3
)
are plotted. What will be the coordinates of point D if ABCD forms a square?
A graph is shown in the xy-plane. The values on the x-axis ranges from negative 8 to 8 in increments of 2 and the values on the y-axis ranges from negative 8 to 8 in increments of 2. Three points Upper A, Upper B, and Upper C are marked on the graph. The point Upper A is 4 units above the x-axis and 4 units to the right of the y-axis. The point Upper B is 4 units above the x-axis and 2 units to the left of the y-axis. The point Upper C is 3 units below the x-axis and 2 units to the left of the y-axis.
To form a square, the distance between all pairs of adjacent points must be equal.
Since AB has a length of 6 (2 units + 4 units), then CD must also have a length of 6. CD is parallel to AB (since it is a square), so the y-coordinate of D is the same as the y-coordinate of C, which is -3.
To find the x-coordinate of D, we need to add 6 to the x-coordinate of C, since the distance from C to D is 6 and the x-coordinates of C and D are the same. So:
x-coordinate of D = x-coordinate of C + 6 = (-2) + 6 = 4
Therefore, the coordinates of point D are (4, -3).
The temperature increased steadily from 6 AM to 2 PM. What will the graph of the data look like?
The graph of the temperature increasing steadily from 6 AM to 2 PM would be a line that slants upwards from left to right, with the x-axis representing time and the y-axis representing temperature.
The line would start at a lower temperature value at 6 AM and steadily slope upwards to a higher temperature value at 2 PM. There may be some slight fluctuations in temperature over time, but the overall trend would be upwards and steady.
The resulting graph would resemble a line with a positive slope, gradually increasing as time passes.