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.

Please show all steps.

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.

Please show all steps.

compassionate · Answer

Hi, cupcake_sarahk You want to verify it is a parallelogram by using the distance formula. In a parallelogram, opposite sides will be equal to one another. Once you find the distance, you can put it in a ratio. A Rhombus has equal opposite sides. If the ratio of the opposite sides are equal, then it is a Rhombus. For more information about the distance formula, please visit: http://www.purplemath.com/modules/distform.htm Regards, OpenStudy Ambassador, OpenStudy Team.