Question

are the lines perpendicular? no, because the slopes of the lines are equal no, because the slopes of the lines are not opposite reciprocals yes, because the slopes of the lines are equal yes, because the slopes of the lines are opposite reciprocals (-8,11) (8,8) (-8,2) (0, -9)

Explanation:

Step1: Calculate slope of first line

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For the line with points $(-8,2)$ and $(8,8)$, we have $x_1=-8,y_1 = 2,x_2=8,y_2 = 8$. Then $m_1=\frac{8 - 2}{8-(-8)}=\frac{6}{16}=\frac{3}{8}$.

Step2: Calculate slope of second line

For the line with points $(-8,11)$ and $(0,-9)$, we have $x_1=-8,y_1 = 11,x_2=0,y_2=-9$. Then $m_2=\frac{-9 - 11}{0-(-8)}=\frac{-20}{8}=-\frac{5}{2}$.

Step3: Check perpendicular - slope condition

Two lines are perpendicular if $m_1\times m_2=- 1$. Here, $m_1\times m_2=\frac{3}{8}\times(-\frac{5}{2})=-\frac{15}{16}
eq - 1$. So the lines are not perpendicular because their slopes are not opposite reciprocals.

Answer:

no, because the slopes of the lines are not opposite reciprocals