Question

The four vertices of a quadrilateral are R(-3,2), S(-1,6), T(3,5) and U(1,1) . What type of quadrilateral is A B C D ? Use calculations to support your answer.

Answer 1

The given quadrilateral is a parallelogram based on the equal slopes of opposite sides.

Step-by-step explanation:

The given quadrilateral has vertices at R(-3,2), S(-1,6), T(3,5), and U(1,1). To determine the type of quadrilateral, we can calculate the slopes of the opposite sides of the quadrilateral. If the slopes of opposite sides are equal, then it is a parallelogram. If the slopes of adjacent sides are equal, then it is a trapezoid. If none of these conditions are met, then it is a general quadrilateral.

Calculating the slopes of each side:

RS: slope = (6 - 2)/(-1 - (-3)) = 4/2 = 2

ST: slope = (5 - 6)/(3 - (-1)) = -1/4

TU: slope = (1 - 5)/(1 - 3) = -4/-2 = 2

UR: slope = (2 - 1)/(-3 - 1) = 1/-4 = -1/4

Since the slopes of opposite sides RS and TU are equal (slope[RS] = 2 and slope[TU] = 2), the quadrilateral is a parallelogram based on its slopes.