Given:
M(4,2) is the midpoint of AB and A(-5, -3).
To find:
The coordinates of 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]
M(4,2) is the midpoint of AB and A(-5, -3).
[tex]M=\left(\dfrac{-5+a}{2},\dfrac{-3+b}{2}\right)[/tex]
[tex](4,2)=\left(\dfrac{-5+a}{2},\dfrac{-3+b}{2}\right)[/tex]
On comparing both sides, we get
[tex]4=\dfrac{-5+a}{2}[/tex]
[tex]8=-5+a[/tex]
[tex]8+5=a[/tex]
[tex]13=a[/tex]
And,
[tex]2=\dfrac{-3+b}{2}[/tex]
[tex]4=-3+b[/tex]
[tex]4+3=b[/tex]
[tex]7=b[/tex]
Therefore, the coordinates of point B are (13,7).
