Question

The midpoint of segment AB has the coordinates M(-4,2). If the coordinates of endpoint A are (-6, -7), find the coordinates of endpoint B.​

Answer 1

Given:

The midpoint of segment AB has the coordinates M(-4,2).

The coordinates of endpoint A are (-6, -7).

To find:

The coordinates of B.

Solution:

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

Formula for midpoint:

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

The midpoint of segment AB has the coordinates M(-4,2), so by using the above formula we get

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

$(-4,2)=\left(\dfrac{-6+a}{2},\dfrac{-7+b}{2}\right)$

On comparing both sides, we get

$\dfrac{-6+a}{2}=-4$

$-6+a=-8$

$a=-8+6$

$a=-2$

And,

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

$-7+b=4$

$b=4+7$

$b=11$

Therefore, the coordinates of point B are (-2,11).