Question

quadrilateral $abcd$ has the following vertices:
$a(2,7)$
$b(8,1)$
$c(1, - 9)$
$d(-6,-2)$
is quadrilateral $abcd$ a parallelogram, and why?
choose 1 answer:

Explanation:

Step1: Calculate slope of AB

Use slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. For $A(2,7)$ and $B(8,1)$, $m_{AB}=\frac{1 - 7}{8 - 2}=\frac{-6}{6}=-1$.

Step2: Calculate slope of CD

For $C(1,-9)$ and $D(-6,-2)$, $m_{CD}=\frac{-2-(-9)}{-6 - 1}=\frac{-2 + 9}{-7}=\frac{7}{-7}=-1$.

Step3: Calculate slope of BC

For $B(8,1)$ and $C(1,-9)$, $m_{BC}=\frac{-9 - 1}{1 - 8}=\frac{-10}{-7}=\frac{10}{7}$.

Step4: Calculate slope of AD

For $A(2,7)$ and $D(-6,-2)$, $m_{AD}=\frac{-2 - 7}{-6 - 2}=\frac{-9}{-8}=\frac{9}{8}$.

Step5: Check parallel - side condition

In a parallelogram, opposite sides are parallel (equal slopes). Since $m_{AB}=m_{CD}=-1$ and $m_{BC}
eq m_{AD}$, quadrilateral $ABCD$ is not a parallelogram.

Answer:

No, because only one pair of opposite - sides has equal slopes.