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

`B = (8,-6)`

Explanation:

Given

`A = (4,8)`

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

Required

Find B

This question will be solved using midpoint formula;

`M(x,y) = ((x_1 + x_2)/(2),(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) = ((4 + x_2)/(2),(8+y_2)/(2))`

By comparison; we have:

`(4 + x_2)/(2) = 6` -- (1)

`(8 + y_2)/(2) = 1` -- (2)

Solving (1)

`(4 + x_2)/(2) = 6`

Multiply both sides by 2

`4 + x_2 = 12`

Subtract 4 from both sides

`x_2 = 8`

Solving (2)

`(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)`