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

(-3,6).

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:

[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

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

[tex]B=\left(\dfrac{a+(-3)}{2},\dfrac{b+6}{2}\right)[/tex]

[tex](0,5.5)=\left(\dfrac{a-3}{2},\dfrac{b+6}{2}\right)[/tex]

On comparing both sides, we get

[tex]\dfrac{a-3}{2}=0[/tex]

[tex]a-3=0[/tex]

[tex]a=3[/tex]

and,

[tex]\dfrac{b+6}{2}=5.5[/tex]

[tex]b+6=11[/tex]

[tex]b=11-6[/tex]

[tex]b=5[/tex]

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

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