Question

Using this graph, how would adding 6+2 6 + 2 then dividing by 2 2 help you find the midpoint of line AB¯¯¯¯¯¯¯¯ 𝐴 𝐵 ¯ ? (1 point) Responses 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 distance between points A and B. It finds the distance between 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 average distance between the two y-values of points A and B. A = (2,-2) B= (6,5)

Answer 1

To find the midpoint of line segment AB, we use the midpoint formula, which states that the midpoint \( M \) of a line segment connecting two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

In your case, the points \( A \) and \( B \) are given as:
- \( A = (2, -2) \)
- \( B = (6, 5) \)

Now, we can find the x-coordinate of the midpoint:

1. Add the x-coordinates of points A and B: \( 2 + 6 = 8 \)
2. Divide by 2 to find the average: \( \frac{8}{2} = 4 \)

Next, we can find the y-coordinate of the midpoint:

1. Add the y-coordinates of points A and B: \( -2 + 5 = 3 \)
2. Divide by 2 to find the average: \( \frac{3}{2} = 1.5 \)

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

To answer the multiple-choice question:

The correct response is: **It finds the sole midpoint of points A and B.**