Given:
Coordinates of point A are (2,8).
Point M(-2,2) is the midpoint of AC.
To find:
The coordinates of C.
Solution:
Let the coordinates of point C 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(2,8) and C(a,b) is
[tex]M=\left(\dfrac{2+a}{2},\dfrac{8+b}{2}\right)[/tex]
[tex](-2,2)=\left(\dfrac{2+a}{2},\dfrac{8+b}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{2+a}{2}=-2[/tex]
[tex]2+a=-4[/tex]
[tex]a=-4-2[/tex]
[tex]a=-6[/tex]
and,
[tex]\dfrac{8+b}{2}=2[/tex]
[tex]8+b=4[/tex]
[tex]b=4-8[/tex]
[tex]b=-4[/tex]
Therefore, the coordinates of point c are (-6,-4).
