Question

quadrilateral abcd has the following vertices: a(-3,0) b(7,2) c(1,-4) d(-9,-6) is quadrilateral abcd a parallelogram, and why? choose 1 answer: a yes, because \\(\overline{ab}\parallel\overline{cd}\\), and \\(\overline{bc}\perp\overline{ab}\\). b yes, because \\(\overline{ab}\parallel\overline{cd}\\), and \\(\overline{bc}\parallel\overline{ad}\\)

Explanation:

Step1: Calculate the slope of line - segment AB

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $A(-3,0)$ and $B(7,2)$, $m_{AB}=\frac{2 - 0}{7-(-3)}=\frac{2}{10}=\frac{1}{5}$.

Step2: Calculate the slope of line - segment CD

For points $C(1,-4)$ and $D(-9,-6)$, $m_{CD}=\frac{-6 - (-4)}{-9 - 1}=\frac{-2}{-10}=\frac{1}{5}$.

Step3: Calculate the slope of line - segment BC

For points $B(7,2)$ and $C(1,-4)$, $m_{BC}=\frac{-4 - 2}{1 - 7}=\frac{-6}{-6}=1$.

Step4: Calculate the slope of line - segment AD

For points $A(-3,0)$ and $D(-9,-6)$, $m_{AD}=\frac{-6 - 0}{-9-(-3)}=\frac{-6}{-6}=1$.

Step5: Determine if it's a parallelogram

Since $m_{AB}=m_{CD}=\frac{1}{5}$, so $\overline{AB}\parallel\overline{CD}$. Since $m_{BC}=m_{AD}=1$, so $\overline{BC}\parallel\overline{AD}$. A quadrilateral with both pairs of opposite - sides parallel is a parallelogram.

Answer:

B. Yes, because $\overline{AB}\parallel\overline{CD}$, and $\overline{BC}\parallel\overline{AD}$