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:

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

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

$B=\left(\dfrac{a+(-3)}{2},\dfrac{b+6}{2}\right)$

$(0,5.5)=\left(\dfrac{a-3}{2},\dfrac{b+6}{2}\right)$

On comparing both sides, we get

$\dfrac{a-3}{2}=0$

$a-3=0$

$a=3$

and,

$\dfrac{b+6}{2}=5.5$

$b+6=11$

$b=11-6$

$b=5$

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