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: *identify the diagonals of the parrallelogram *compute the slope of each diagonal *explain how you know the parallelogram is a rhombus

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.