Question

The coordinates of point T are (0,3). The midpoint or ST is (1,4). Find the coordinates of point S.

The other endpoint is _

(type an ordered pair)

Answer 1

`S = (2,5)`

Explanation:

Given

`T = (0,3)`

`Midpoint (M) =(1,4)`

Required

Determine the other end point (S)

Midpoint is calculated as thus:

`M(x,y) = ((S_x + T_x)/(2),(S_y + T_y)/(2))`

This gives:

`(1,4) = ((S_x + 0)/(2),(S_y + 3)/(2))`

`(1,4) = ((S_x)/(2),(S_y + 3)/(2))`

Multiply through by 2

`2 * (1,4) = ((S_x)/(2),(S_y + 3)/(2)) * 2`

`(2,8) = (S_x,S_y + 3)`

By comparison:

`S_x = 2`

`S_y + 3 = 8`

`S_y = 8 - 3`

`S_y = 5`

Hence:

The coordinates of S is

`S = (2,5)`