Answer:
The coordinates of the other end is ![(16,2)](https://tex.z-dn.net/?f=%2816%2C2%29)
Step-by-step explanation:
Given
![End 1: (-6,2)](https://tex.z-dn.net/?f=End%201%3A%20%28-6%2C2%29)
![Midpoint: (5,2)](https://tex.z-dn.net/?f=Midpoint%3A%20%285%2C2%29)
Required
Find the coordinates of the other end
Let Midpoint be represented by (x,y);
(x,y) = (5,2) is calculated as thus
![(x,y) = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%28%5Cfrac%7Bx_1%20%2B%20x_2%7D%7B2%7D%2C%5Cfrac%7By_1%20%2B%20y_2%7D%7B2%7D%29)
So
and ![y = \frac{y_1 + y_2}{2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7By_1%20%2B%20y_2%7D%7B2%7D)
Where
and ![(x,y) = (5,2)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%285%2C2%29)
So, we're solving for ![(x_2,y_2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29)
Solving for ![x_2](https://tex.z-dn.net/?f=x_2)
Substitute 5 for x and -6 for x₁
![5 = \frac{-6 + x_2}{2}](https://tex.z-dn.net/?f=5%20%3D%20%5Cfrac%7B-6%20%2B%20x_2%7D%7B2%7D)
Multiply both sides by 2
![2 * 5 = \frac{-6 + x_2}{2} * 2](https://tex.z-dn.net/?f=2%20%2A%205%20%3D%20%5Cfrac%7B-6%20%2B%20x_2%7D%7B2%7D%20%2A%202)
![10 = -6 + x_2](https://tex.z-dn.net/?f=10%20%3D%20-6%20%2B%20x_2)
Add 6 to both sides
![6 + 10 = -6 +6 + x_2](https://tex.z-dn.net/?f=6%20%2B%2010%20%3D%20-6%20%2B6%20%2B%20%20x_2)
![x_2 = 16](https://tex.z-dn.net/?f=x_2%20%3D%2016)
Solving for ![y_2](https://tex.z-dn.net/?f=y_2)
![y = \frac{y_1 + y_2}{2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7By_1%20%2B%20y_2%7D%7B2%7D)
Substitute 2 for y and 2 for y₁
![2 = \frac{2 + y_2}{2}](https://tex.z-dn.net/?f=2%20%3D%20%5Cfrac%7B2%20%2B%20y_2%7D%7B2%7D)
Multiply both sides by 2
![2 * 2 = \frac{2 + y_2}{2} * 2](https://tex.z-dn.net/?f=2%20%2A%202%20%3D%20%5Cfrac%7B2%20%2B%20y_2%7D%7B2%7D%20%2A%202)
![4 = 2 + y_2](https://tex.z-dn.net/?f=4%20%3D%202%20%2B%20y_2)
Subtract 2 from both sides
![4 - 2 = 2 - 2 + y_2](https://tex.z-dn.net/?f=4%20-%202%20%3D%202%20-%202%20%2B%20y_2)
![y_2 = 2](https://tex.z-dn.net/?f=y_2%20%3D%202)
![(x_2,y_2) = (16,2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%2816%2C2%29)
Hence, the coordinates of the other end is ![(16,2)](https://tex.z-dn.net/?f=%2816%2C2%29)