Question 353868
HI,  
*Note: showing the quadrilateral ABCD has all four interior angles 90° (right angles) can be done by showing the adjacent sides 
are perpendicular to on another, by showing the slopes of the lines containing their respective coordinates are negative reciprocals.
.
using the point-slope form:
 {{{m =(y[2] - y[1])/(x[2] - x[1])}}}
.
A (-1,5)   B(7,1)
{{{m =(1- 5)/(7 - (-1))= ( -1/2)}}}.
.
B(7,1) C(5, -3)
 {{{m =((-3)- 1)/(5 - 7)= 2}}}. 
AB IS PERPENDICULAR TO BC
.
C(5, -3)  D(-3,1)
{{{m =(1 -(-3))/(-3 - 5)= (-1/2)}}}.
BC IS PERPENDICULAR TO CD 
.
D(-3,1)  A (-1,5) 
{{{m =(5 -1)/(-1 - 4)= 2}}}.
DA IS PERPENDICULAR TO AB