The other endpoint is (31, -4)
Solution:
Given that midpoint (23,- 10), endpoint (15.-16)
To find: The other endpoint
The formula for midpoint is given as:
[tex]\text {For two points }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right), \text { the midpoint }(x, y) \text { is given as: }[/tex]
[tex]m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]
Here in this problem,
[tex]m(x, y) = (23, -10)[/tex]
[tex](x_1, y_1) = (15, -16)[/tex]
[tex](x_2, y_2) = ?[/tex]
Substituting the values in formula we get,
[tex](23,-10)=\left(\frac{15+x_{2}}{2}, \frac{-16+y_{2}}{2}\right)[/tex]
On comparing both sides we get,
[tex]23=\frac{15+x_{2}}{2} \text { and }-10=\frac{-16+y_{2}}{2}[/tex]
[tex]\begin{array}{l}{46=15+x_{2} \text { and }-20=-16+y_{2}} \\\\ {x_{2}=46-15 \text { and } y_{2}=-20+16} \\\\ {x_{2}=31 \text { and } y_{2}=-4}\end{array}[/tex]
Thus the other endpoint is (31, - 4)