Coordinate Proofs Math Example 1

Solution

1. 1
   Step 1: Assign coordinates strategically. Place the rectangle with vertices at $A(0,0)$, $B(a,0)$, $C(a,b)$, and $D(0,b)$, where $a,b > 0$.
2. 2
   Step 2: Find the length of diagonal $AC$ using the distance formula: $AC = \sqrt{(a-0)^2 + (b-0)^2} = \sqrt{a^2+b^2}$.
3. 3
   Step 3: Find the length of diagonal $BD$: $BD = \sqrt{(0-a)^2 + (b-0)^2} = \sqrt{a^2+b^2}$.
4. 4
   Step 4: Since $AC = BD = \sqrt{a^2+b^2}$, the diagonals of the rectangle are equal in length. $\blacksquare$