Question

The midpoint of AB is M (6,1). If the coordinates of A are (4, 8), what are the coordinates of B?

Answer 1

Answer:

$B = (8,-6)$

Step-by-step explanation:

Given

$A = (4,8)$

$M = (6,1)$ -- Midpoint

Required

Find B

This question will be solved using midpoint formula;

$M(x,y) = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$

Where

$A(x_1,y_1) = (4,8)$

$M(x,y) = (6,1)$

Substitute these values in the midpoint formula;

$(6,1) = (\frac{4 + x_2}{2},\frac{8+y_2}{2})$

By comparison; we have:

$\frac{4 + x_2}{2} = 6$ -- (1)

$\frac{8 + y_2}{2} = 1$ -- (2)

Solving (1)

$\frac{4 + x_2}{2} = 6$

Multiply both sides by 2

$4 + x_2 = 12$

Subtract 4 from both sides

$x_2 = 8$

Solving (2)

$\frac{8 + y_2}{2} = 1$

Multiply both sides by 2

$8 + y_2 = 2$

Subtract 8 from both sides

$y_2 = -6$

Hence:

$B = (8,-6)$