Question

given p (0,0) q(3,4) s(7,4) and y(4,0). use the slope formula to determine if pqsy is a parallelogram.
the slope of $overline{pq}$ = select choice $\boldsymbol{downarrow}$, the slope of $overline{qs}$= select choice $\boldsymbol{downarrow}$, the slope of $overline{sy}$= select choice $\boldsymbol{downarrow}$, and the slope of $overline{yp}$= select choice $\boldsymbol{downarrow}$
therefore, pqsy select choice $\boldsymbol{downarrow}$ a parallelogram because select choice $\boldsymbol{downarrow}$

Explanation:

Step1: Calculate slope of $\overline{PQ}$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m_{PQ}=\frac{4-0}{3-0}=\frac{4}{3}$

Step2: Calculate slope of $\overline{QS}$

$m_{QS}=\frac{4-4}{7-3}=\frac{0}{4}=0$

Step3: Calculate slope of $\overline{SY}$

$m_{SY}=\frac{0-4}{4-7}=\frac{-4}{-3}=-\frac{4}{3}$

Step4: Calculate slope of $\overline{YP}$

$m_{YP}=\frac{0-0}{0-4}=\frac{0}{-4}=0$

Step5: Verify parallelogram condition

Opposite slopes: $m_{PQ}=m_{SY}$, $m_{QS}=m_{YP}$; so opposite sides are parallel.

Answer:

Slope of $\overline{PQ} = \frac{4}{3}$, Slope of $\overline{QS} = 0$, Slope of $\overline{SY} = -\frac{4}{3}$, Slope of $\overline{YP} = 0$
Therefore, PQSY is a parallelogram because both pairs of opposite sides are parallel