Use the image to answer the question.

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, you would use the midpoint formula, which calculates the average of the x-coordinates and the average of the y-coordinates of the endpoints A and B.

In your question, when you add the y-values (which are -2 and 5 for points A and B), you calculate:

\( \text{Midpoint y-coordinate} = \frac{(-2) + 5}{2} = \frac{3}{2} = 1.5 \)

Similarly, for the x-values (which are 2 and 6), you would calculate:

\( \text{Midpoint x-coordinate} = \frac{2 + 6}{2} = \frac{8}{2} = 4 \)

Thus, the correct response to the question about how adding 6 + 2 and then dividing by 2 helps you find the midpoint of line AB is:

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

So the correct option is:

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