Question

If (4,-3) is the midpoint of the line segment ST and the coordinates of S are (1,5), find the

coordinates of T.

Answer 1

`(7,-11)`

Explanation:

Given

`S = (1,5)`

`M = (4,-3)`

Required

Determine the coordinates of T

Midpoint is calculated as:

`M(x,y) = (1)/(2)(x_1 +x_2,y_1+y_2)`

Where:

`(x,y) = (4,-3)`

`(x_1,y_1) = (1,5)`

Substitute these values in the above formula:

`(4,-3) = (1)/(2)(1 + x_2,5+y_2)`

Multiply through by 2

`2 * (4,-3) = 2 * (1)/(2)(1 + x_2,5+y_2)`

`(8,-6) = (1 + x_2,5+y_2)`

By direct comparison:

`1 + x_2 = 8` and
`5 + y_2 = -6`

Solving for x2

`1 + x_2 = 8`

`x_2 = 8 - 1`

`x_2 = 7`

Solving for y2

`5 + y_2 = -6`

`y_2 = -6 - 5`

`y_2 = -11`

Hence, the coordinates of T is:
`(7,-11)`