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 ⋄.

Explanation:

Step1: Calculate slope of AB

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
For $A(-4,-5), B(-3,0)$:
$m_{AB}=\frac{0-(-5)}{-3-(-4)}=\frac{5}{1}=5$

Step2: Calculate slope of DC

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

Step3: Calculate slope of BC

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

Step4: Calculate slope of AD

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

Answer:

Slope of AB: $5$
Slope of DC: $-\frac{1}{5}$
Slope of BC: $\frac{2}{3}$
Slope of AD: $\frac{2}{3}$
Since $m_{BC}=m_{AD}$, $\overline{BC} \parallel \overline{AD}$, so quadrilateral ABCD is a trapezoid.