The points plotted on the coordinate plane below are three vertices of a rectangle. What are the coordinates of the fourth vertex of the rectangle?
Without seeing the coordinates of the three given vertices, I cannot provide an answer. Please provide the coordinates or a diagram.
The points plotted on the coordinate plane below are three vertices of a rectangle. Three points plotted on a Cartesian grid include left-parenthesis negative two point five comma two right-parenthesis, left-parenthesis one comma two right-parenthesis, left-parenthesis one comma negative one right-parenthesis.
To find the fourth vertex of the rectangle, we can use the fact that opposite sides of a rectangle are parallel and have the same length.
First, let's find the distance between the two given points on the x-axis:
1 - (-2.5) = 3.5
So the length of the rectangle is 3.5 units.
Next, let's find the distance between the two given points on the y-axis:
2 - (-1) = 3
So the width of the rectangle is 3 units.
Now we can use this information to find the coordinates of the fourth vertex. Since the rectangle is symmetrical with respect to its center, we can find the center of the rectangle as the midpoint between the two given points:
x-coordinate of center = (-2.5 + 1)/2 = -0.75
y-coordinate of center = (2 - 1)/2 = 0.5
So the center of the rectangle is (-0.75, 0.5).
To find the fourth vertex, we can add or subtract the width and length from the center:
Adding the length and width: (-0.75 + 3.5/2, 0.5 + 3/2) = (1.25, 2.5)
Subtracting the length and width: (-0.75 - 3.5/2, 0.5 - 3/2) = (-4, -1)
Therefore, the coordinates of the fourth vertex of the rectangle are either (1.25, 2.5) or (-4, -1), depending on which direction the rectangle is oriented.
Which of these is correct?
(-1, -2.5)
(-2, -2.5)
(-2.5, -1)
(-2.5, -2)
None of these is necessarily correct, as there is not enough information to determine the exact location of the fourth vertex of the rectangle. The correct answer is:
(1.25, 2.5) or (-4, -1)
depending on which direction the rectangle is oriented.
The points plotted on the coordinate plane below are three vertices of a rectangle. Three points plotted on a Cartesian grid include left-parenthesis negative two point five comma two right-parenthesis, left-parenthesis one comma two right-parenthesis, left-parenthesis one comma negative one right-parenthesis.
Which of these is correct?
(-1, -2.5)
(-2, -2.5)
(-2.5, -1)
(-2.5, -2)
None of these coordinates is correct. To find the fourth vertex of the rectangle, we need to use the given vertices to determine the length and width of the rectangle, and then find the location of the fourth vertex using that information.
The length of the rectangle is the distance between the points (-2.5, 2) and (1, 2) on the x-axis, which is 1 - (-2.5) = 3.5 units.
The width of the rectangle is the distance between the points (1, 2) and (1, -1) on the y-axis, which is 2 -(-1) = 3 units.
The center of the rectangle is the midpoint of the segment connecting (-2.5, 2) and (1, -1), which is ((-2.5+1)/2, (2-1)/2) = (-0.75,0.5).
The fourth vertex of the rectangle can be found by adding or subtracting half the length and half the width from the center, giving us two possible locations for the fourth vertex:
(-0.75 - 1.75, 0.5 + 1.5) = (-2.5, 2)
(-0.75 + 1.75, 0.5 - 1.5) = (1, -1)
Therefore, the two possible coordinates for the fourth vertex of the rectangle are (-2.5, 2) and (1, -1).
The endpoints of four segments are given below. Which segment has the greatest length?
A (2, 2) and B (2, -4)
D (-3, -1) and E (2, -1)
M (-1, 4) and N (-1, -2)
P (-5, -3) and Q (2, -3)
We can find the length of each segment using the distance formula:
Length of segment AB = sqrt[(2 - 2)^2 + (-4 - 2)^2] = 6
Length of segment DE = sqrt[(-3 - 2)^2 + (-1 - (-1))^2] = 5
Length of segment MN = sqrt[(-1 - (-1))^2 + (4 - (-2))^2] = 6
Length of segment PQ = sqrt[(-5 - 2)^2 + (-3 - (-3))^2] = 7
Therefore, segment PQ has the greatest length of 7 units.
The table below shows the relationships between the numbers of hot dogs sold, x, and the profits made, y, in dollars.
Input Output
0 -1
3 8
10 29
Which equation represents the rule for the function table?
y=x-1
y=x+5
y=3x-1
y=2x-1
We can find the equation that represents the rule for the function table by using the given input-output pairs.
First, we can find the slope (m) of the line that passes through the points (0, -1) and (3, 8) using the slope formula:
m = (change in y) / (change in x) = (8 - (-1)) / (3 - 0) = 9/3 = 3
Next, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is a point on the line. We can choose either of the given points as (x1, y1), but using (0, -1) yields a simpler equation:
y - (-1) = 3(x - 0)
y + 1 = 3x
Subtracting 1 from both sides, we get:
y = 3x - 1
Therefore, the equation that represents the rule for the function table is y = 3x - 1.
Which graph shows the solution to the inequality?
x-5<-2
A number line ranges from negative 5 to 5 and has an open point at 3 with an arrow pointing from 3 to the left. A number line ranges from negative 5 to 5 and has an open point at 3 with an arrow pointing from 3 to the right. A number line ranges from negative 5 to 5 has a closed point at 3 with an arrow pointing from 3 to the left. A number line ranges from negative 5 to 5 and has a closed point at 3 with an arrow pointing from 3 to the right.
The inequality x - 5 < -2 can be solved for x by adding 5 to both sides:
x - 5 + 5 < -2 + 5
x < 3
This means that all values of x that are less than 3 satisfy the inequality.
Therefore, the solution to the inequality is represented by a number line that ranges from negative 5 to 5 and has an open point at 3 with an arrow pointing from 3 to the left.
The correct graph is the first option:
A number line ranges from negative 5 to 5 and has an open point at 3 with an arrow pointing from 3 to the left.