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.

Hope this attached file will help u.

 To know if Diagonals are perpendicular we need to know two line's slope
If two lines are pependicular their slope m1×m2=-1

For if they are making rhombus two opposite equal sides so u need to know the distancebetween the points.