IF (-6, 4) is the endpoint of a line segment, and (-2, -1) is its midpoint, find the other endpoint.
1 answer:
A midpoint has coordinates of
we will call them
.
The coordinates of a midpoint are constructed from coordinates of enpoints
, namely as a divided sum.
![x_m=\frac{x_1+x_2}{2}\implies x_1=2x_m-x_2 \\y_m=\frac{y_1+y_2}{2}\implies y_1=2y_m-y_2](https://tex.z-dn.net/?f=%3C%2Fp%3E%3Cp%3Ex_m%3D%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%5Cimplies%20x_1%3D2x_m-x_2%20%5C%5C%3C%2Fp%3E%3Cp%3Ey_m%3D%5Cfrac%7By_1%2By_2%7D%7B2%7D%5Cimplies%20y_1%3D2y_m-y_2%3C%2Fp%3E%3Cp%3E)
Now insert the numbers.
![x_1=2(-2)-(-6)=2 \\y_1=2(-1)-4=-6](https://tex.z-dn.net/?f=%3C%2Fp%3E%3Cp%3Ex_1%3D2%28-2%29-%28-6%29%3D2%20%5C%5C%3C%2Fp%3E%3Cp%3Ey_1%3D2%28-1%29-4%3D-6%3C%2Fp%3E%3Cp%3E)
The result is an endpoint at
.
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