Example 2: Verify that the diagonals of the square with vertices A(-2,-1),B(2,-1),C(2,3) and D(-2,3) bisect each other.

## Step 1: Calculate the midpoint of diagonal AC<br />### The midpoint formula is given by $M = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$. For diagonal AC, we have $A(-2,-1)$ and $C(2,3)$. Thus, the midpoint of AC is $M_{AC} = (\frac{-2+2}{2}, \frac{-1+3}{2}) = (0,1)$.<br /><br />## Step 2: Calculate the midpoint of diagonal BD<br />### For diagonal BD, we have $B(2,-1)$ and $D(-2,3)$. Thus, the midpoint of BD is $M_{BD} = (\frac{2+(-2)}{2}, \frac{-1+3}{2}) = (0,1)$.<br /><br />## Step 3: Compare the midpoints<br />### Since $M_{AC} = (0,1)$ and $M_{BD} = (0,1)$, the midpoints of the diagonals are the same. This means the diagonals bisect each other.