Question

Verify that parallelogram ABCD with verticals A(-5,-1),B(-9,6),C(-1,5),and D(3,-2) is a rhombus. Do the following:

Answer 1

Points A and C are the endpoints of one diagonal. Its slope will be
.. (5-(-1))/(-1-(-5)) = 6/4 = 3/2

Points B and D are the endpoints of the other diagonal. Its slope will be
.. (-2-6)/(3-(-9)) = -8/12 = -2/3

The diagonals cross at right angles, so the figure is a rhombus or a kite.


The midpoints of the diagonals are
.. (A +C)/2 = (-5-1, -1+5)/2 = (-3, 2)
.. (B +D)/2 = (-9+3, 6-2)/2 = (-3, 2)

The midpoints of the diagonals are the same. The diagonals are perpendicular bisectors of each other, so the figure is a rhombus.