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Question

Line segment upper A (2,-2) upper B (6,5) is plotted on a coordinate plane. The x-axis ranges from 0 to 7 and the y-axis ranges from negative 3 to 7 both in one unit increments.

Using this graph, how would adding 6+2 then dividing by 2 help you find the midpoint of line AB¯¯¯¯¯¯¯¯ ?

(1 point)
Responses

It finds the average distance between the two y-values of points A and B.
It finds the average distance between the two y -values of points A and B.

It finds the average distance between the two x-values of points A and B.
It finds the average distance between the two x -values of points A and B.

It finds the sole midpoint of points A and B.
It finds the sole midpoint of points A and B.

It finds the distance between points A and B.
It finds the distance between points A and B.
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Answer 1

To find the midpoint of line segment AB, we need to calculate the average of the x-coordinates and the average of the y-coordinates of points A and B.

For points A(2, -2) and B(6, 5):

• The x-coordinates are 2 and 6.
• The y-coordinates are -2 and 5.

To find the midpoint coordinates \((x_m, y_m)\):

1. For the x-coordinate of the midpoint: \[ x_m = \frac{x_1 + x_2}{2} = \frac{2 + 6}{2} = \frac{8}{2} = 4 \]

2. For the y-coordinate of the midpoint: \[ y_m = \frac{y_1 + y_2}{2} = \frac{-2 + 5}{2} = \frac{3}{2} = 1.5 \]

Therefore, the midpoint of line segment AB is (4, 1.5).

Regarding the responses provided, the correct one related to adding 6 + 2 and then dividing by 2 would be:

"It finds the average distance between the two x-values of points A and B."

This describes that the calculation of \((6 + 2)/2\) finds the average of the x-values of points A (2) and B (6), which is necessary for determining the x-coordinate of the midpoint.