Question

Use the slope to determine if lines AB and CD are parallel, perpendicular, or neither. A(-3, 8), B(3, 2), C(7, 1), D(5, -1)

A) Lines AB and CD are parallel.
B) Lines AB and CD are perpendicular.
C) Lines AB and CD are neither parallel nor perpendicular.
D) More information is needed to determine their relationship.

Answer 1

The lines AB and CD are neither parallel nor perpendicular.

Step-by-step explanation:

To determine if lines AB and CD are parallel, perpendicular, or neither, we can calculate the slopes of the lines. The slope of a line can be found using the formula m = (y2-y1)/(x2-x1), where (x1, y1) and (x2, y2) are two points on the line.

For line AB, using the points A(-3, 8) and B(3, 2), the slope is m = (2-8)/(3-(-3)) = -6/6 = -1.

For line CD, using the points C(7, 1) and D(5, -1), the slope is m = (-1-1)/(5-7) = -2/(-2) = 1.

Since the slopes of the two lines are not equal and they are not negative reciprocals of each other, the lines AB and CD are neither parallel nor perpendicular.