Question

The midpoint of AB is M(3,3). If the coordinates of A are (2, -1), what are the

coordinates of B?

Answer 1

Answer:(4,7)

Explanation:

Answer 2

(4, 7)

Explanation:

Given:

Midpoint of AB = M(3, 3)

A(2, -1)

Required:

Coordinates of B

SOLUTION:

let
`A(2, -1) = (x_2, y_2)`

`B(?, ?) = (x_1, y_1)`

`M(3, 3) = ((x_1 + 2)/(2), (y_1 +(-1))/(2))`

Rewrite the equation to find the coordinates of B

`3 = (x_1 + 2)/(2)` and
`3 = (y_1 - 1)/(2)`

Solve for each:

`3 = (x_1 + 2)/(2)`

`3*2 = (x_1 + 2)/(2)*2`

`6 = x_1 + 2`

`6 - 2 = x_1 + 2 - 2`

`4 = x_1`

`x_1 = 4`

`3 = (y_1 - 1)/(2)`

`3*2 = (y_1 - 1)/(2)*2`

`6 = y_1 - 1`

`6 + 1 = y_1 - 1 + 1`

`7 = y_1`

`y_1 = 7`

Coordinates of B is (4, 7)