Question

The midpoint of AB is M (2,0). If the coordinates of A are, (-3, 3), what are the coordinates of B?​

Answer 1

Given:

M is the midpoint of AB.

M(2,0) and A(-3, 3).

To find:

The coordinates of point B.

Solution:

Midpoint formula:

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

Let the coordinates of point B are (a,b). Then, using the midpoint formula, we get

$(2,0)=\left(\dfrac{-3+a}{2},\dfrac{3+b}{2}\right)$

On comparing both sides, we get

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

$-3+a=2\times 2$

$a=4+3$

$a=7$

And,

$\dfrac{3+b}{2}=0$

$3+b=0$

$3+b-3=0-3$

$b=-3$

Therefore, the coordinates of point B are (7,-3).