### Instruction: Points $(1,-5)$ and $(11,7)$ are the opposite vertices of a parallelogram.  What are the coordinates of the point where the diagonals of the parallelogram intersect?### Response: So we have the two points (1,-5) and (11,7).
And we know that the diagonals of a parallelogram intersect at their midpoints.
Right. So we need to find the midpoint of these two points.
We do that by finding the average of their x and y coordinates.
So the x-coordinate of the midpoint is $(1+11)/2=6$.
The y-coordinate of the midpoint is $(-5+7)/2=1$.