# A line segment has an endpoint at (4, 6), the midpoint of the line segment is (1, 5). What are the coordinates of the point at the other end of the line segment?

The other end is at $\left(- 2 , 4\right)$.
I look at the change in each of the $x$ and $y$ directions. From the given endpoint to the midpoint, the segment moves $- 3$ in the $x$ direction and $- 1$ in the $y$ direction.
To find the other endpoint, just move the same way from the midpoint. From $\left(1 , 5\right)$: $\left(1 - 3 , 5 - 1\right) = \left(- 2 , 4\right) .$