Verify that parallelogram ABCD with vertices A ( - 5, - 1), B ( - 9, 6), C ( - 1, 5), and D (3, - 2) 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.

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Mathematics

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31 October, 03:10

Verify that parallelogram ABCD with vertices A ( - 5, - 1), B ( - 9, 6), C ( - 1, 5), and D (3, - 2) 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.

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Anderson Hunt · Answer 1

Step-by-step explanation:

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.