Question

The midpoint of overline AB is M(0, - 7) . If coordinates of A are (- 2, - 6) , what are the coordinates of B?

Answer 1

Given:

The midpoint of overline AB is M(0, - 7) .

The coordinates of A are (- 2, - 6).

To find:

The coordinates of point B.

Solution:

Let the coordinates of point B are (a,b).

Midpoint formula:

`Midpoint=\left((x_1+x_2)/(2),(y_1+y_2)/(2)\right)`

The midpoint of overline AB is M(0, - 7). Using the midpoint formula, we get

`M=\left((-2+a)/(2),(-6+b)/(2)\right)`

`(0,-7)=\left((-2+a)/(2),(-6+b)/(2)\right)`

On comparing both sides, we get

`(-2+a)/(2)=0`

`-2+a=0`

`a=2`

And,

`(-6+b)/(2)=-7`

`-6+b=-14`

`b=-14+6`

`b=-8`

Therefore, the coordinates of point B are (2,-8).