Question

6.3.12

The coordinates of point T are (0,5). The midpoint of ST is (2,-2). Find the coordinates of point S.
The other endpoint is
(Type an ordered pair.)

Answer 1

`S = (4,-9)`

Explanation:

Given

`T = (0,5)`

`Midpoint = (2,-2)`

Required

Find S

Midpoint is calculated as:

`Midpoint = 0.5(x_1 + x_2,y_1+y_2)`

So, we have:

`(2,-2)= 0.5(0+ x_2,5+y_2)`

Where x2 and y2 are the coordinates of S

Multiply through by 2

`2 * (2,-2)= 2 * 0.5(0+ x_2,5+y_2)`

`(4,-4)= (0+ x_2,5+y_2)`

`(4,-4)= (x_2,5+y_2)`

By comparison:

`x_2 = 4`

`5 + y_2 = -4`

`y_2 = -4-5`

`y_2 = -9`

So:

`S = (4,-9)`