On a coordinate plane, square P Q R S is shown. It has points (0, 4), (4, 4), (0, 0), and (4, 0).
Prove the diagonals of the square with vertices P(0, 4), Q(4, 4), R(0, 0), and S(4, 0) are perpendicular bisectors of each other.
Step 1: Calculate the slope of the diagonals.
The slope of diagonal PS is
.
The slope of diagonal QR is
Step 2: Calculate the midpoint of the diagonals.
The midpoint of PS is
The midpoint of QR is
.
The diagonals of the square are perpendicular bisectors because the diagonals are
