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

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

`M=\left((-5+a)/(2),(-3+b)/(2)\right)`

`(4,2)=\left((-5+a)/(2),(-3+b)/(2)\right)`

On comparing both sides, we get

`4=(-5+a)/(2)`

`8=-5+a`

`8+5=a`

`13=a`

And,

`2=(-3+b)/(2)`

`4=-3+b`

`4+3=b`

`7=b`

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