which statement best explains the relationship between lines pq and rs? they are parallel because their…

which statement best explains the relationship between lines pq and rs? they are parallel because their slopes are equal. they are parallel because their slopes are negative reciprocals. they are not parallel because their slopes are not equal. they are not parallel because their slopes are negative reciprocals.

which statement best explains the relationship between lines pq and rs? they are parallel because their slopes are equal. they are parallel because their slopes are negative reciprocals. they are not parallel because their slopes are not equal. they are not parallel because their slopes are negative reciprocals.

Answer

Explanation:

Step1: Encontrar la pendiente de la línea PQ

Sean $P(-5,3)$ y $Q(5,1)$. La fórmula de la pendiente $m = \frac{y_2 - y_1}{x_2 - x_1}$. Entonces $m_{PQ}=\frac{1 - 3}{5-(-5)}=\frac{-2}{10}=-\frac{1}{5}$.

Step2: Encontrar la pendiente de la línea RS

Sean $R(-5,-2)$ y $S(0,-4)$. La pendiente $m_{RS}=\frac{-4 - (-2)}{0-(-5)}=\frac{-4 + 2}{5}=\frac{-2}{5}=-\frac{2}{5}$.

Step3: Comprobar la relación entre las pendientes

Como $m_{PQ}=-\frac{1}{5}$ y $m_{RS}=-\frac{2}{5}$, $m_{PQ}\neq m_{RS}$.

Answer:

They are not parallel because their slopes are not equal.