Question

Q8
The midpoint of GH is M (2,2). One endpoint is H (1,9). Find the coordinates of endpoint G.

Answer 1

(3,-5)

Explanation:

Given

`M = (2,2)`

`H = (1,9)`

Required

Determine G

This is calculated using the following midpoint formula;

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

Where

`(x,y) = (2,2)` and
`(x_1,y_1) = (1,9)`

Substitute these values in the formula above

`(2,2) = ((1 + x_2)/(2),(9 + y_2)/(2))`

Solving for
`x_2`

`2 =(1 + x_2)/(2)`

Multiply both sides by 2

`2 * 2 = 1 + x_2`

`4 = 1 + x_2`

`x_2 = 4 - 1`

`x_2 = 3`

Solving for
`y_2`

`2 = (9 + y_2)/(2)`

Multiply both sides by 2

`2 * 2 = 9 + y_2`

`4 = 9 + y_2`

`y_2 = 4 - 9`

`y_2= -5`

Hence, the coordinates of G is
`(3,-5)`