Question

Line A passes through the points (0,2) and (2,−2). Line B passes through the points (0,4) and (1,2). Line C passes through the points (0,−1) and (4,1). Identify which lines are parallel and which lines are perpendicular.

Answer 1

Answer:

Line A and B are parallel and line C is perpendicular to both A and B.

Step-by-step explanation:

To determine if lines are parallel or perpendicular, recall:

• Parallel lines have the same slope.
• Perpendicular lines have negative reciprocal slope.

Find the slope through the formula $m = \frac{y_2-y_1}{x_2-x_1}$.

Line A

$m = \frac{y_2-y_1}{x_2-x_1}=\frac{2--2}{0-2}=\frac{2+2}{-2}=\frac{4}{-2}=-2$

Line B

$m = \frac{y_2-y_1}{x_2-x_1}=\frac{4-2}{0-1}=\frac{2}{-1}=-2$

Line C

$m = \frac{y_2-y_1}{x_2-x_1}=\frac{1--1}{4-0}=\frac{1+1}{4}=\frac{2}{4}=\frac{1}{2}$

Line A and B are parallel and Line C is perpendicular to both A and B.