Question

Help
Me plz and thank you

Answer 1

B. (-1, -3)

Explanation:

Given M(1, -4) as midpoint of
`\overline{GH}`, and G(3, -5),

let
`G(3, -5) = (x_2, y_2)`

`H(?, ?) = (x_1, y_1)`

`M(1, -4) = ((x_1 + 3)/(2), (y_1 +(-5))/(2))`

Rewrite the equation to find the coordinates of G

`1 = (x_1 + 3)/(2)` and
`-4 = (y_1 - 5)/(2)`

Solve for each:

`1 = (x_1 + 3)/(2)`

Multiply both sides by 2

`1*2 = (x_1 + 3)/(2)*2`

`2 = x_1 + 3`

Subtract 3 from each side

`2 - 3 = x_1 + 3 - 3`

`-1 = x_1`

`x_1 = -1`

`-4 = (y_1 - 5)/(2)`

Multiply both sides by 2

`-4*2 = (y_1 - 5)/(2)*2`

`-8 = y_1 - 5`

Add 5 to both sides

`-8 + 5 = y_1 - 5 + 5`

`-3 = y_1`

`y_1 = -3`

Coordinates of G is (-1, -3)