Question

A polygon has vertices whose coordinates are A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1). Use the midpoint formula to determine whether or not the diagonals of polygon ABCD bisect each other. In your final answer, include all of your calculations.

Answer 1

Explanation:

midpoint of AC

`x=(1-1)/(2) =0\\y=(4-4)/(2) =0\\mid ~point~of~AC=(0,0)`

midpoint of BD

`x=(4-4)/(2) =0\\y=(-1+1)/(2) =0\\midpoint ~of~BD=(0,0)`

so diagonals bisect each other.