The coordinates of other endpoint S is (3, 2)
<h3><u>Solution:</u></h3>
Given that midpoint of RS is M
Given endpoint R(23, 14) and midpoint M(13, 8)
To find: coordinates of the other endpoint S
<em><u>The formula for midpoint is given as:</u></em>
For a line containing containing two points
and
midpoint is given as:
![m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)](https://tex.z-dn.net/?f=m%28x%2C%20y%29%3D%5Cleft%28%5Cfrac%7Bx_%7B1%7D%2Bx_%7B2%7D%7D%7B2%7D%2C%20%5Cfrac%7By_%7B1%7D%2By_%7B2%7D%7D%7B2%7D%5Cright%29)
Here in this problem,
m(x, y) = (13, 8)
![(x_1, y_1) = (23, 14)\\\\(x_2, y_2) = ?](https://tex.z-dn.net/?f=%28x_1%2C%20y_1%29%20%3D%20%2823%2C%2014%29%5C%5C%5C%5C%28x_2%2C%20y_2%29%20%3D%20%3F)
Substituting the given values in above formula, we get
![(13,8)=\left(\frac{23+x_{2}}{2}, \frac{14+y_{2}}{2}\right)](https://tex.z-dn.net/?f=%2813%2C8%29%3D%5Cleft%28%5Cfrac%7B23%2Bx_%7B2%7D%7D%7B2%7D%2C%20%5Cfrac%7B14%2By_%7B2%7D%7D%7B2%7D%5Cright%29)
Comparing both the sides we get,
![\begin{aligned}&13=\frac{23+x_{2}}{2} \text { and } 8=\frac{14+y_{2}}{2}\\\\&26=23+x_{2} \text { and } 16=14+y_{2}\\\\&x_{2}=3 \text { and } y_{2}=2\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%2613%3D%5Cfrac%7B23%2Bx_%7B2%7D%7D%7B2%7D%20%5Ctext%20%7B%20and%20%7D%208%3D%5Cfrac%7B14%2By_%7B2%7D%7D%7B2%7D%5C%5C%5C%5C%2626%3D23%2Bx_%7B2%7D%20%5Ctext%20%7B%20and%20%7D%2016%3D14%2By_%7B2%7D%5C%5C%5C%5C%26x_%7B2%7D%3D3%20%5Ctext%20%7B%20and%20%7D%20y_%7B2%7D%3D2%5Cend%7Baligned%7D)
Thus the coordinates of other endpoint S is (3, 2)