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A quadrilateral has vertices at A(−5, 5), B(1, 8), C(4, 2), and D(−2, −2).
Use slope to determine if the quadrilateral is a rectangle. Show your work.
(4 points)
To determine if the quadrilateral is a rectangle, we need to check if the diagonals are perpendicular to each other. If the product of the slopes of the diagonals is -1, then the quadrilateral is a rectangle.
First, let's find the slopes of the diagonals:
Diagonal AC: Slope = (2-5)/(4-(-5)) = -3/9 = -1/3
Diagonal BD: Slope = (-2-8)/(-2-1) = -10/-3 = 10/3
Next, let's find the product of the slopes:
(-1/3)*(10/3) = -10/9
Since the product of the slopes is not -1, the quadrilateral is not a rectangle.
Therefore, the quadrilateral with vertices A(−5, 5), B(1, 8), C(4, 2), and D(−2, −2) is not a rectangle.