Question

Use the image to answer the 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 which answer is correct and why

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 need to calculate the average of the x-values and the average of the y-values of points A and B.

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

1. To find the midpoint, you first find the average of the x-values:
\[
\text{Midpoint x} = \frac{x_1 + x_2}{2} = \frac{2 + 6}{2} = \frac{8}{2} = 4
\]

2. Next, you find the average of the y-values:
\[
\text{Midpoint y} = \frac{y_1 + y_2}{2} = \frac{-2 + 5}{2} = \frac{3}{2} = 1.5
\]

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

Based on the options provided, the statement that relates to this process is:

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

The reason this is correct is that when you add the x-values (2 and 6), and then divide by 2, you are indeed finding the average (or midpoint) of the x-coordinates of points A and B. The wording in the option about "distance" may be misleading; it’s not about finding the physical distance between the points but rather their average position.