Aquadrilateral has vertices at a(–5, 5), b(1, 8), c(4, 2), d(–2, –2). use slope to determine if the quadrilateral is a rectangle. show your work.

With the properties of rectangle in mind we must perform two verification. Verify to see if opposite sides are parallel and adjacent sides are perpendicular.

We need to determine the slope of each side, using the formula,

Slope  of AB

Slope of BC

Slope of CD

Slope of AD

Verify Parallel sides

If the quadrilateral is a rectangle, then opposite sides should have the same slope. But

Verify Perpendicularity

And also the product of slopes of all sides with a common vertex should be -1. But

Since the quadrilateral fails to satisfy all these conditions, the quadrilateral is not a rectangle

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step-by-step explanation: