Answer:
B. (8, 1)
Step-by-step explanation:
Given M(6, 5) as midpoint of PQ, and P(4, 9),
let [tex] P(4, 9) = (x_2, y_2) [/tex]
[tex] Q(?, ?) = (x_1, y_1) [/tex]
[tex] M(6, 5) = (\frac{x_1 + 4}{2}, \frac{y_1 + 9}{2}) [/tex]
Rewrite the equation to find the coordinates of Q (x1, y1):
[tex] 6 = \frac{x_1 + 4}{2} [/tex] and [tex] 5 = \frac{y_1 + 9}{2} [/tex]
Solve for each:
[tex] 6 = \frac{x_1 + 4}{2} [/tex]
Multiply both sides by 2
[tex] 6*2 = \frac{x_1 + 4}{2}*2 [/tex]
[tex] 12 = x_1 + 4 [/tex]
Subtract 4 from both sides
[tex] 12 - 4 = x_1 + 4 - 4 [/tex]
[tex] 8 = x_1 [/tex]
[tex] x_1 = 8 [/tex]
[tex] 5 = \frac{y_1 + 9}{2} [/tex]
Multiply both sides by 2
[tex] 5*2 = \frac{y_1 + 9}{2}*2 [/tex]
[tex] 10 = y_1 + 9 [/tex]
Subtract 9 from both sides
[tex] 10 - 9 = y_1 + 9 - 9 [/tex]
[tex] 1 = y_1 [/tex]
[tex] y_1 = 1 [/tex]
Coordinates of Q is (8, 1)
