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:

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

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

$M=\left(\dfrac{-2+a}{2},\dfrac{-6+b}{2}\right)$

$(0,-7)=\left(\dfrac{-2+a}{2},\dfrac{-6+b}{2}\right)$

On comparing both sides, we get

$\dfrac{-2+a}{2}=0$

$-2+a=0$

$a=2$

And,

$\dfrac{-6+b}{2}=-7$

$-6+b=-14$

$b=-14+6$

$b=-8$

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