+385 A map of the town that Annie and Barbara live in can be represented by the Cartesian plane. Annie is located at $(5,-11)$ and Barbara says she is located at $(-7,13)$. They agree to meet at the midpoint of the segment formed by their current locations. However, it turns out that Barbara read the map wrong, and Barbara is actually at $(-5,5)$. What is the positive difference in the $y$-coordinates of where they agreed to meet and where they should actually meet?
+41 Since the problem only asks for the difference in the \(y \)-coordinates, we can ignore the \(x\)-coordinates.
They originally agreed to meet at the midpoint of \((5,-11)\) and \((-7,13)\), so the -coordinate of the planned location is \( \frac{-11+13}{2}=1\).
The correct meeting location should be at the midpoint of \((5,-11)\) and \((-5,5)\), so the -coordinate should be at \(\frac{-11+5}{2}=-3\). The positive difference is \(1-(-3)=\boxed{4}\).
Alternatively, notice that an 8-unit change in the y-coordinate of Barbara's location resulted in a 4-unit change in the midpoint since the 8 gets divided by 2. \(\frac{-11+5}{2}=\frac{-11+13}{2}-\frac{8}{2}=1-\boxed{4}\).
