Question

The vertices of quadrilateral ABCD are, A(-7,10), B(1,2), C(-6,-6), and D(-14,2). A) Use slope calculations to classify the quadrilateral as parallelogram, rectangle, trapezoid, or quadrilateral.

Answer 1

By calculating the slopes of its sides, we can determine that quadrilateral ABCD is a parallelogram.

Step-by-step explanation:

To determine the classification of quadrilateral ABCD, we can use the slopes of its sides. First, we calculate the slopes of lines AB, BC, CD, and DA using the formula 'slope = (change in y)/(change in x)'.

The slope of AB = (2 - 10)/(1 - (-7)) = -8/8 = -1.

The slope of BC = (-6 - 2)/(-6 - 1) = -8/-7 ≈ 1.14.

The slope of CD = (2 - (-6))/(-14 - (-6)) = 8/-8 = -1.

The slope of DA = (10 - 2)/(-7 - (-14)) = 8/7 ≈ 1.14.

Since opposite sides have equal slopes, we can conclude that quadrilateral ABCD is a parallelogram.