Answer:
The coordinates of B are (10,2)
Step-by-step explanation:
Hi there!
We know that BC has a midpoint M, with the coordinates (6,6), and the endpoint C, with coordinates (2, 10)
We want to find the coordinates of point B
The midpoint formula is
, where
and
are points. In this case, the point C has the values of
, and B has the values of ![(x_2 , y_2)](https://tex.z-dn.net/?f=%28x_2%20%2C%20y_2%29)
We know that coordinates of M equal ![(\frac{x_1 + x_2}{2}, \frac{y_1+ y_2}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7Bx_1%20%2B%20x_2%7D%7B2%7D%2C%20%5Cfrac%7By_1%2B%20y_2%7D%7B2%7D%29)
In other words,
![\frac{x_1 + x_2}{2} = 6\\ \frac{y_1+ y_2}{2}=6](https://tex.z-dn.net/?f=%5Cfrac%7Bx_1%20%2B%20x_2%7D%7B2%7D%20%3D%206%5C%5C%20%5Cfrac%7By_1%2B%20y_2%7D%7B2%7D%3D6)
Let's plug 2 for
and 10 for ![y_1](https://tex.z-dn.net/?f=y_1)
So:
![\frac{2 + x_2}{2} = 6\\ \frac{10+ y_2}{2}=6](https://tex.z-dn.net/?f=%5Cfrac%7B2%20%2B%20x_2%7D%7B2%7D%20%3D%206%5C%5C%20%5Cfrac%7B10%2B%20y_2%7D%7B2%7D%3D6)
Multiply both sides by 2
![{2 + x_2} = 12\\{10+ y_2} =12](https://tex.z-dn.net/?f=%7B2%20%2B%20x_2%7D%20%3D%2012%5C%5C%7B10%2B%20y_2%7D%20%3D12)
Subtract 2 from both sides in the first equation to find the value of
:
![x_2=10](https://tex.z-dn.net/?f=x_2%3D10)
Now, for the second equation, subtract 10 from both sides to find the value of ![y_2](https://tex.z-dn.net/?f=y_2)
![y_2=2](https://tex.z-dn.net/?f=y_2%3D2)
Now substitute these values for ![(x_2, y_2)](https://tex.z-dn.net/?f=%28x_2%2C%20y_2%29)
![(x_2, y_2)=(10,2)](https://tex.z-dn.net/?f=%28x_2%2C%20y_2%29%3D%2810%2C2%29)
So the coordinates of point B are (10, 2)
Hope this helps!