### Instruction: Segment $s_1$ has endpoints at $(4,1)$ and $(-8,5)$.  Segment $s_2$ is obtained by translating $s_1$ by $2$ units to the right and $3$ units up. Find the midpoint of segment $s_2$.  Express your answer as $(a,b)$ with $a$ and $b$ integers.### Response: Ok, so we need to find the midpoint of the segment that is obtained by translating the segment between $(4,1)$ and $(-8,5)$ by $2$ units to the right and $3$ units up.
Let's start by finding the midpoint of the original segment.
Ok.  The original segment is between $(4,1)$ and $(-8,5)$.
So the midpoint is at $\left(\frac{4-8}{2},\frac{1+5}{2}\right)$, which is $(-2,3)$.
Now we need to translate this point by $2$ units to the right and $3$ units up.
That gives us $(-2+2,3+3)$, which is $(0,6)$.