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

All the  slope of quadrilateral ABCD  calculated by using formula of slope.Given:A quadrilateral ABCD with vertices A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1).We have to calculate the slope of AB, DC, BC, AD.By using formula of slope,[tex]Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]Now, calculate the slope of AB,A(–4, –5), B(–3, 0), put this value in (1)[tex]Slope=\dfrac{0-(-5)}{-3-(-4)}= \dfrac{5}{1} =5[/tex]Calculate the slope of DC,C(0, 2), D(5, 1), put this value in (1)[tex]Slope=\dfrac{2-1}{0-5}= \dfrac{-1}{5}[/tex]Calculate the slope of BC, B(–3, 0), C(0, 2), put this value in (1)[tex]Slope=\dfrac{2-0}{0-(-3)}= \dfrac{2}{3}[/tex]Calculate the slope of AD,A(–4, –5), D(5, 1), put this value in (1)[tex]Slope=\dfrac{1-(-5)}{5-(-4)}= \dfrac{6}{9}= \dfrac{2}{3}[/tex] For  further details, please prefer this link: