Question

1. hint, you will need to find the slope for all 4 lines first

line a: (-9,-12), (-2,2)
line b: (-5,3), (-4,6)
line c: (2,3), (-1,4)
line d: (-1,6), (-5,-2)
which lines are parallel?
which lines are perpendicular?

Explanation:

Step1: Recall slope formula

The slope formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate slope of Line A

For Line A with points $(-9,-12)$ and $(-2,2)$, $m_A=\frac{2-(-12)}{-2-(-9)}=\frac{2 + 12}{-2 + 9}=\frac{14}{7}=2$.

Step3: Calculate slope of Line B

For Line B with points $(-5,3)$ and $(-4,6)$, $m_B=\frac{6 - 3}{-4-(-5)}=\frac{6 - 3}{-4 + 5}=\frac{3}{1}=3$.

Step4: Calculate slope of Line C

For Line C with points $(2,3)$ and $(-1,4)$, $m_C=\frac{4 - 3}{-1 - 2}=\frac{1}{-3}=-\frac{1}{3}$.

Step5: Calculate slope of Line D

For Line D with points $(-1,6)$ and $(-5,-2)$, $m_D=\frac{-2 - 6}{-5-(-1)}=\frac{-2 - 6}{-5 + 1}=\frac{-8}{-4}=2$.

Step6: Determine parallel lines

Parallel lines have equal slopes. Since $m_A = 2$ and $m_D=2$, Line A and Line D are parallel.

Step7: Determine perpendicular lines

Perpendicular lines have slopes that are negative - reciprocals of each other. Since $m_B = 3$ and $m_C=-\frac{1}{3}$, Line B and Line C are perpendicular.

Answer:

Parallel lines: Line A and Line D
Perpendicular lines: Line B and Line C