Analytic Geometry Math Example 2

Solution

1. 1
   Place the rectangle with vertices at $A(0,0)$, $B(a,0)$, $C(a,b)$, $D(0,b)$ where $a,b>0$.
2. 2
   Find the midpoint of diagonal $AC$: $M_1 = \left(\frac{0+a}{2}, \frac{0+b}{2}\right) = \left(\frac{a}{2}, \frac{b}{2}\right)$.
3. 3
   Find the midpoint of diagonal $BD$: $M_2 = \left(\frac{a+0}{2}, \frac{0+b}{2}\right) = \left(\frac{a}{2}, \frac{b}{2}\right)$.
4. 4
   Since $M_1 = M_2$, the diagonals share the same midpoint, so they bisect each other.