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 all opposite sides are parallel all sides are perpendicular only one pair of opposite sides is parallel

Explanation:

Step1: Calculate slope of AB

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $A(-4,-5)$ and $B(-3,0)$, we have $m_{AB}=\frac{0 - (-5)}{-3-(-4)}=\frac{5}{1} = 5$.

Step2: Calculate slope of DC

For points $D(5,1)$ and $C(0,2)$, $m_{DC}=\frac{2 - 1}{0 - 5}=\frac{1}{-5}=-\frac{1}{5}$.

Step3: Calculate slope of BC

For points $B(-3,0)$ and $C(0,2)$, $m_{BC}=\frac{2 - 0}{0-(-3)}=\frac{2}{3}$.

Step4: Calculate slope of AD

For points $A(-4,-5)$ and $D(5,1)$, $m_{AD}=\frac{1-(-5)}{5 - (-4)}=\frac{6}{9}=\frac{2}{3}$.

Answer:

The slope of AB is 5.
The slope of DC is $-\frac{1}{5}$.
The slope of BC is $\frac{2}{3}$.
The slope of AD is $\frac{2}{3}$.
The quadrilateral is a trapezoid because only one pair of opposite sides is parallel (BC and AD since $m_{BC}=m_{AD}=\frac{2}{3}$).