Question

Given M is the midpoint ABA. The coordinate of A are (-4,2) and the cordinates of M are (1,1). Find the coordinate of B. Choose (-2,4) (-2,0) (6,4) (6,0)

Answer 1

The coordinate of B is (6,0)

Explanation:

Given;

coordinate of A = (-4,2) = (x₁, y₁)

coordinate of M = (1,1)

let coordinate of B = (x₂, y₂)

Mid-point is given by;

`M = (X_1 + X_2)/(2) , (Y_1 + Y_2)/(2)\\\\M= (1,1)\\\\1,1 =(X_1 + X_2)/(2) , (Y_1 + Y_2)/(2)\\\\ (X_1 + X_2)/(2) = 1 ----equation (1)\\\\(Y_1 + Y_2)/(2) = 1 -----equation(2)\\\\Solving \ equation(1)\\\\(-4+ X_2)/(2) = 1\\\\-4+ X_2 = 2\\\\X_2 = 2+4\\\\X_2 = 6\\\\Solving \ equation(2)\\\\(Y_1 + Y_2)/(2) = 1\\\\(2+ Y_2)/(2) = 1\\\\2+Y_2 = 2\\\\Y_2 = 2-2\\\\Y_2 = 0\\\\B = (X_2, \ Y_2)\\\\B = (6, \ 0)`

Therefore, the coordinate of B is (6,0)