Question

Midpoint (23,- 10), endpoint (15.-16) The other endpoint is

Answer 1

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:

$\text {For two points }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right), \text { the midpoint }(x, y) \text { is given as: }$

$m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Here in this problem,

$m(x, y) = (23, -10)$

$(x_1, y_1) = (15, -16)$

$(x_2, y_2) = ?$

Substituting the values in formula we get,

$(23,-10)=\left(\frac{15+x_{2}}{2}, \frac{-16+y_{2}}{2}\right)$

On comparing both sides we get,

$23=\frac{15+x_{2}}{2} \text { and }-10=\frac{-16+y_{2}}{2}$

$\begin{array}{l}{46=15+x_{2} \text { and }-20=-16+y_{2}} \\\\ {x_{2}=46-15 \text { and } y_{2}=-20+16} \\\\ {x_{2}=31 \text { and } y_{2}=-4}\end{array}$

Thus the other endpoint is (31, - 4)