Question

The coordinates of the midpoint of a segment are (3,7). If the coordinates of one endpoint are (-2, 4), find the coordinates of the other endpoint.

a. (1,5)
b. (8,10)
c. (7,3)
d. (0,1)

Answer 1

The coordinates of the other endpoint are (8, 10)

Step-by-step explanation:

Given the coordinates of the midpoint (3, 7) and one endpoint (-2, 4), we can find the coordinates of the other endpoint using the midpoint formula. The midpoint formula states that the x-coordinate of the midpoint is equal to the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is equal to the average of the y-coordinates of the endpoints.

x-coordinate of the other endpoint = (2 * x-coordinate of the midpoint) - x-coordinate of one endpoint = (2 * 3) - (-2) = 6 + 2 = 8

y-coordinate of the other endpoint = (2 * y-coordinate of the midpoint) - y-coordinate of one endpoint = (2 * 7) - 4 = 14 - 4 = 10

Therefore, the coordinates of the other endpoint are (8, 10). So, the correct answer is (b) (8, 10).