Answer:
(4, 7)
Step-by-step explanation:
Given:
Midpoint of AB = M(3, 3)
A(2, -1)
Required:
Coordinates of B
SOLUTION:
let [tex] A(2, -1) = (x_2, y_2) [/tex]
[tex] B(?, ?) = (x_1, y_1) [/tex]
[tex] M(3, 3) = (\frac{x_1 + 2}{2}, \frac{y_1 +(-1)}{2}) [/tex]
Rewrite the equation to find the coordinates of B
[tex] 3 = \frac{x_1 + 2}{2} [/tex] and [tex] 3 = \frac{y_1 - 1}{2} [/tex]
Solve for each:
[tex] 3 = \frac{x_1 + 2}{2} [/tex]
[tex] 3*2 = \frac{x_1 + 2}{2}*2 [/tex]
[tex] 6 = x_1 + 2 [/tex]
[tex] 6 - 2 = x_1 + 2 - 2 [/tex]
[tex] 4 = x_1 [/tex]
[tex] x_1 = 4 [/tex]
[tex] 3 = \frac{y_1 - 1}{2} [/tex]
[tex] 3*2 = \frac{y_1 - 1}{2}*2 [/tex]
[tex] 6 = y_1 - 1 [/tex]
[tex] 6 + 1 = y_1 - 1 + 1 [/tex]
[tex] 7 = y_1 [/tex]
[tex] y_1 = 7 [/tex]
Coordinates of B is (4, 7)
