A quadrilateral has vertices A (3, 5), B (2, 0), C (7, 0), and D (8, 5). Which statement about the quadrilateral is true?

Question

Mathematics

Curry

11 June, 07:36

A quadrilateral has vertices A (3, 5), B (2, 0), C (7, 0), and D (8, 5). Which statement about the quadrilateral is true?

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Answers (1)

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Maddison · Answer 1

It is a parallelogram.

Step-by-step explanation:

The opposite sides AD and BC are both horizontal so they are parallel.

The slope o AB = (0-5) / (2-3) = 5 and slope of the opposite side CD =

(5-0) / (8-7) = 5 so these 2 are also parallel.

The quadrilateral is therefore a parallelogram.

If 2 adjacent sides are equal it is also a rhombus so we check the lengths of the sides.

Length of AD = 8-3 = 5 units.

Length of DC = sqrt ((5-0) ^2 + (8-7) ^2) = sqrt 26 so it is not a rhombus.