Question

A line segment has an endpoint at (3, 2). If the midpoint of the line segment is (6, -2), what are the coordinates of the point at the other end of the line segment?

a) (4.5, 0)
b) (0, 6)
c) (9, -6)
d) (9, 4)

Answer 1

To find the coordinates of the other end of the line segment, we can use the midpoint formula. The coordinates of the other end of the line segment are (9, -6).

Step-by-step explanation:

To find the coordinates of the other end of the line segment, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment are the average of the coordinates of its endpoints. In this case, the midpoint is (6, -2). So, we can set up the following equation:

(3 + x)/2 = 6

(2 + y)/2 = -2

Simplifying these equations, we get:

3 + x = 12

2 + y = -4

Solving for x and y, we find that the coordinates of the other end of the line segment are (9, -6). Therefore, the correct answer is c) (9, -6).