Question

- Find the coordinates of A if B(0,5.5) is the midpoint of AC and C has coordinates

(-3,6).

Answer 1

Given:

Coordinates of point C are (-3,6).

Point B(0,5.5) is the midpoint of AC.

To find:

The coordinates of A.

Solution:

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

Formula for midpoint:

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

Using the above formula, the midpoint of A(a,b) and C(-3,6) is

`B=\left((a+(-3))/(2),(b+6)/(2)\right)`

`(0,5.5)=\left((a-3)/(2),(b+6)/(2)\right)`

On comparing both sides, we get

`(a-3)/(2)=0`

`a-3=0`

`a=3`

and,

`(b+6)/(2)=5.5`

`b+6=11`

`b=11-6`

`b=5`

Therefore, the coordinates of point A are (3,5).