Answer:
B. (-1, -3)
Step-by-step explanation:
Given M(1, -4) as midpoint of [tex] \overline{GH} [/tex], and G(3, -5),
let [tex] G(3, -5) = (x_2, y_2) [/tex]
[tex] H(?, ?) = (x_1, y_1) [/tex]
[tex] M(1, -4) = (\frac{x_1 + 3}{2}, \frac{y_1 +(-5)}{2}) [/tex]
Rewrite the equation to find the coordinates of G
[tex] 1 = \frac{x_1 + 3}{2} [/tex] and [tex] -4 = \frac{y_1 - 5}{2} [/tex]
Solve for each:
[tex] 1 = \frac{x_1 + 3}{2} [/tex]
Multiply both sides by 2
[tex] 1*2 = \frac{x_1 + 3}{2}*2 [/tex]
[tex] 2 = x_1 + 3 [/tex]
Subtract 3 from each side
[tex] 2 - 3 = x_1 + 3 - 3 [/tex]
[tex] -1 = x_1 [/tex]
[tex] x_1 = -1 [/tex]
[tex] -4 = \frac{y_1 - 5}{2} [/tex]
Multiply both sides by 2
[tex] -4*2 = \frac{y_1 - 5}{2}*2 [/tex]
[tex] -8 = y_1 - 5 [/tex]
Add 5 to both sides
[tex] -8 + 5 = y_1 - 5 + 5 [/tex]
[tex] -3 = y_1 [/tex]
[tex] y_1 = -3 [/tex]
Coordinates of G is (-1, -3)
