Verify that parallelogram abcd with vertices a(-5 -1) b(-9,6) c(-1,5) d(3,-2) is a rhombus by showing that it is a parallelogram with perpendicular diagonals

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Step-by-step explanation:  Given vertices of parallelogram abcd are a(-5,-1), b(-9,6), c(-1,5) and d(3,-2).

Since it is a parallelogram, so opposite sides must be equal. That is,

ab = cd,  bc = ad.

We are to show abcd is a rhombus by showing that the diagonals ac and bd are perpendicular to each other.

Now,

So, ab = bc = cd = da, with proves that all the sides are equal.

Now, slope of diagonal ac will be

and the slope of bd will be

Therefore,

This shows that the diagonals ac and bd are perpendicular.

Thus, the parallelogram abcd is a rhombus.

is there any attachment? what are the equations?