Question

What are the coordinates of the other endpoint of a segment if one endpoint is at A(12, 4) and the midpoint is at M(17, -3)?

Answer 1

The coordinates of the other endpoint of the segment are (7, 11).

Step-by-step explanation:

To find the coordinates of the other endpoint of a segment, we need to use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (M) is the average of the x-coordinates and the average of the y-coordinates of the two endpoints.

Given that one endpoint is at A(12, 4) and the midpoint is at M(17, -3), we can calculate the coordinates of the other endpoint as follows:

1. Subtract the x-coordinate of the midpoint from twice the x-coordinate of the endpoint: 2 * x-coordinate of endpoint - x-coordinate of midpoint = 2 * 12 - 17 = 24 - 17 = 7.
2. Subtract the y-coordinate of the midpoint from twice the y-coordinate of the endpoint: 2 * y-coordinate of endpoint - y-coordinate of midpoint = 2 * 4 - (-3) = 8 + 3 = 11.

Therefore, the coordinates of the other endpoint are (7, 11).