Question

If M (4.2) is the midpoint of AB and A (-5, -3), find the coordinates of B.

Answer 1

Given:

M(4,2) is the midpoint of AB and A(-5, -3).

To find:

The coordinates of B.

Solution:

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

Midpoint formula:

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

M(4,2) is the midpoint of AB and A(-5, -3).

$M=\left(\dfrac{-5+a}{2},\dfrac{-3+b}{2}\right)$

$(4,2)=\left(\dfrac{-5+a}{2},\dfrac{-3+b}{2}\right)$

On comparing both sides, we get

$4=\dfrac{-5+a}{2}$

$8=-5+a$

$8+5=a$

$13=a$

And,

$2=\dfrac{-3+b}{2}$

$4=-3+b$

$4+3=b$

$7=b$

Therefore, the coordinates of point B are (13,7).