Question

Determine whether quadrilateral ABCD with vertices A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1) is a trapezoid. Step 1: Find the slope of AB. The slope of AB is . Step 2: Find the slope of DC. The slope of DC is . Step 3: Find the slope of BC. The slope of BC is . Step 4: Find the slope of AD. The slope AD is . The quadrilateral is a trapezoid because

Answer 1

Slope AB 0-(-5)/-3-(-4)= 0+5/-3+4= 5/1= 5 so Slope AB= 5

And the last fill-in is The quadrilateral is a Trapezoid because ..."Only one pair of opposite sides is parallel"

Answer 2

Answer: Yes, the quadrilateral ABCD is a trapezoid.

Step-by-step explanation: Given that the vertices of the quadrilateral ABCD are A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1).

We are to determine whether ABCD is a trapezoid or not.

We know that a trapezoid is a quadrilateral with one pair of opposite sides parallel. Also, the slopes of two parallel lines are equal.

First, we will find the slopes of the sides AB, BC, CD and DA.

We have

$\textup{Step 1: The slope of AB}=\dfrac{0+5}{-3+4}=\dfrac{5}{1}=5,\\\\\textup{Step 2: The slope of BC}=\dfrac{2-0}{0+3}=\dfrac{2}{3},\\\\\textup{Step 3: The slope of CD}=\dfrac{1-2}{5-0}=-\dfrac{1}{5},\\\\\textup{Step 4: The slope of DA}=\dfrac{-5-1}{-4-5}=\dfrac{2}{3}.$

Since the slopes of the sides BC and DA are equal, so BC an DA are the parallel sides of the quadrilateral ABCD.

Thus, the quadrilateral is a trapezoid because it has a pair of opposite sides parallel.