Given:
The midpoint of overline AB is M(0, - 7) .
The coordinates of A are (- 2, - 6).
To find:
The coordinates of point B.
Solution:
Let the coordinates of point B are (a,b).
Midpoint formula:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
The midpoint of overline AB is M(0, - 7). Using the midpoint formula, we get
[tex]M=\left(\dfrac{-2+a}{2},\dfrac{-6+b}{2}\right)[/tex]
[tex](0,-7)=\left(\dfrac{-2+a}{2},\dfrac{-6+b}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{-2+a}{2}=0[/tex]
[tex]-2+a=0[/tex]
[tex]a=2[/tex]
And,
[tex]\dfrac{-6+b}{2}=-7[/tex]
[tex]-6+b=-14[/tex]
[tex]b=-14+6[/tex]
[tex]b=-8[/tex]
Therefore, the coordinates of point B are (2,-8).
