SOLUTION: The vertices of a Quadrilateral ABCD has coordinates A (-1,5) b(7,1) C(5, -3) and D(-3,1) show that the quadrilateral is a rectangle

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Question 353868: The vertices of a Quadrilateral ABCD has coordinates A (-1,5) b(7,1)
C(5, -3) and D(-3,1)
show that the quadrilateral is a rectangle
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
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+=%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29
.
A (-1,5) B(7,1)
m+=%281-+5%29%2F%287+-+%28-1%29%29=+%28+-1%2F2%29.
.
B(7,1) C(5, -3)
m+=%28%28-3%29-+1%29%2F%285+-+7%29=+2.
AB IS PERPENDICULAR TO BC
.
C(5, -3) D(-3,1)
m+=%281+-%28-3%29%29%2F%28-3+-+5%29=+%28-1%2F2%29.
BC IS PERPENDICULAR TO CD
.
D(-3,1) A (-1,5)
m+=%285+-1%29%2F%28-1+-+4%29=+2.
DA IS PERPENDICULAR TO AB