Question

question 1 (multiple choice worth 4 points) which of the following best classifies a quadrilateral with coordinates a(8, 4), b(6, 0), c(3, 2), and d(7, 10)? trapezoid parallelogram kite rectangle

Explanation:

Step1: Calculate the slopes of the sides

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Slope of $AB$ with $A(8,4)$ and $B(6,0)$: $m_{AB}=\frac{0 - 4}{6 - 8}=\frac{-4}{-2}=2$.
Slope of $BC$ with $B(6,0)$ and $C(3,2)$: $m_{BC}=\frac{2 - 0}{3 - 6}=\frac{2}{-3}=-\frac{2}{3}$.
Slope of $CD$ with $C(3,2)$ and $D(7,10)$: $m_{CD}=\frac{10 - 2}{7 - 3}=\frac{8}{4}=2$.
Slope of $DA$ with $D(7,10)$ and $A(8,4)$: $m_{DA}=\frac{4 - 10}{8 - 7}=\frac{-6}{1}=-6$.

Step2: Analyze parallel - side conditions

Since $m_{AB}=m_{CD}=2$, one pair of opposite sides ($AB$ and $CD$) is parallel.

Answer:

Trapezoid