Question

Help Me plz and thank you

Answer 1

Answer:

B. (-1, -3)

Step-by-step explanation:

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

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

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

$M(1, -4) = (\frac{x_1 + 3}{2}, \frac{y_1 +(-5)}{2})$

Rewrite the equation to find the coordinates of G

$1 = \frac{x_1 + 3}{2}$ and $-4 = \frac{y_1 - 5}{2}$

Solve for each:

$1 = \frac{x_1 + 3}{2}$

Multiply both sides by 2

$1*2 = \frac{x_1 + 3}{2}*2$

$2 = x_1 + 3$

Subtract 3 from each side

$2 - 3 = x_1 + 3 - 3$

$-1 = x_1$

$x_1 = -1$

$-4 = \frac{y_1 - 5}{2}$

Multiply both sides by 2

$-4*2 = \frac{y_1 - 5}{2}*2$

$-8 = y_1 - 5$

Add 5 to both sides

$-8 + 5 = y_1 - 5 + 5$

$-3 = y_1$

$y_1 = -3$

Coordinates of G is (-1, -3)