Question

The midpoint of line AB is (14,26). One endpoint of line AB is A(32, 40). What are the coordinates of B?

A. B(-4,-12)
B. B(0,0)
C. B(-4,12)
D. B(23,33)

Answer 1

The coordinates of the midpoint:

`((x_1+x_2)/(2), (y_1+y_2)/(2))`
(x₁,y₁) - the coordinates of one endpoint
(x₂,y₂) - the coordinates of the other endpoint

The midpoint is (14,26).
One endpoint is A(32,40).
The other endpoint is B.

The x-coordinate of B:

`(32+x)/(2)=14 \ \ \ |* 2 \\ 32+x=28 \ \ \ |-32 \\ x=-4`

The y-coordinate of B:

`(40+y)/(2)=26 \ \ \ |* 2 \\ 40+y=52 \ \ \ |-40 \\ y=12`

The coordinates of B are (-4,12) - the answer is C.