SOLUTION: Verify that parallelogram ABCD with vertices A(–5, –1), B(–9, 6), C(–1, 5), and D(3, –2) is a rhombus by showing that it is a parallelogram with perpendicular diagonals

Algebra ->  Parallelograms -> SOLUTION: Verify that parallelogram ABCD with vertices A(–5, –1), B(–9, 6), C(–1, 5), and D(3, –2) is a rhombus by showing that it is a parallelogram with perpendicular diagonals      Log On


   

Question 550000: Verify that parallelogram ABCD with vertices A(–5, –1), B(–9, 6), C(–1, 5), and D(3, –2) is a rhombus by showing that it is a parallelogram with perpendicular diagonals
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If I choose pairs of points, and the parallelogram
is a rhombus, the slopes of the lines through
these pairs of points will either be parallel
or they will be negative reciprocals of
each other ( perpendicular )
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If will choose the pairs
(1) A(-5,-1) and C(-1,5)
and
(2) B(-9,6) and D(3,-2)
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The slope of pair (1) is
( change in y ) / ( change in x ) = +%285+-%28-1%29%29+%2F+%28-1+-%28-5%29%29+=+6%2F4+
+6%2F4+=+3%2F2+
The slope of pair (2) is
( change in y ) / ( change in x ) = +%28+-2+-+6+%29+%2F+%28+3+-%28-9%29+%29+=+-8%2F12+
+-8%2F12+=+-2%2F3+
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These lines have slopes that are negative reciprocals of each other,
so they are perpendicular, and the parallelogram is a rhombus
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You can also show ( not necessary ) that the pairs of
points AB and CD form lines which are parallel