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

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

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 = (y_2-y_1)/(x_2-x_1)`.

Line A

`m = (y_2-y_1)/(x_2-x_1)=(2--2)/(0-2)=(2+2)/(-2)=(4)/(-2)=-2`

Line B

`m = (y_2-y_1)/(x_2-x_1)=(4-2)/(0-1)=(2)/(-1)=-2`

Line C

`m = (y_2-y_1)/(x_2-x_1)=(1--1)/(4-0)=(1+1)/(4)=(2)/(4)=(1)/(2)`

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