Verify that parallelogram abcd with vertices a(-5,-1) b (-9,6) c(-1,5) and d (3,-2) is a rhombus. do the following •identify the diagonals of the parallelogram •compute the slope of the diagonal •explain how you know the parallelogram is a rhombus

The diagonals of the parallelogram are A(-5, -1), C(-1, 5) and B(-9, 6), D(3, -2).
Slope of diagonal AC = (5 - (-1)) / (-1 - (-5)) = (5 + 1) / (-1 + 5) = 6 / 4 = 3/2
Slope of diagonal BD = (-2 - 6) / (3 - (-9)) = -8 / (3 + 9) = -8 / 12 = -2/3
For the parallelogram to be a rhombus, the intersection of the diagonals are perpendicular.
i.e. the product of the two slopes equals to -1.

Slope AC x slope BD = 3/2 x -2/3 = -1.
Therefore, the parallelogram is a rhombus.