Answer
See proof
Work Step by Step
The slope of the first diagonal is
$m_1 = \frac{\Delta y}{\Delta x} = \frac{-1 -5}{4 - (-2)} = \frac{-6}{6} = -1$
The slope of the second diagonal is
$m_2 = \frac{5 - (-1)}{4 - (-2)} = \frac{6}{6} = 1$.
For two lines to be perpendicular we must have
$m_2 = \frac{-1}{m_1}$.
The slopes calculated fulfill this equation:
$1 = \frac{-1}{-1}$
and thus the diagonals are perpendicular.
