Question

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 1

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.