Given:
One endpoint of a line segment = (-7,-9)
Midpoint of the segment = (-2,-16)
To find:
The other endpoint of the given line segment.
Solution:
Let (a,b) be the other endpoint of the given line segment.
Midpoint formula:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
Using this formula, we get
[tex](-2,-16)=\left(\dfrac{-7+a}{2},\dfrac{-9+b}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{-7+a}{2}=-2[/tex]
[tex]-7+a=-4[/tex]
[tex]a=-4+7[/tex]
[tex]a=3[/tex]
And,
[tex]\dfrac{-9+b}{2}=-16[/tex]
[tex]-9+b=-32[/tex]
[tex]b=-32+9[/tex]
[tex]b=-23[/tex]
Therefore, the coordinates of other endpoint are (3,-23).
