Question

PQ: P(5,2) Q(-1,6)

AB: A(-2,3) B (4,-1)

A. Parallel
B. Perpendicular
C. Neither
D. Skew

Answer 1

The lines defined by the points given are parallel since they both have the same slope of -2/3.

Step-by-step explanation:

To determine the relationship between two lines, we can compare the slopes of the lines formed by the points given. If the slopes are equal, the lines are parallel; if the slopes are negative reciprocals of each other, the lines are perpendicular; if neither condition is met, the lines are neither parallel nor perpendicular.

The slope of PQ can be calculated using the coordinates of P and Q:

• Slope of PQ = (y2 - y1) / (x2 - x1) = (6 - 2) / (-1 - 5) = 4 / -6 = -2/3

The slope of AB can be calculated using the coordinates of A and B:

• Slope of AB = (y2 - y1) / (x2 - x1) = (-1 - 3) / (4 - (-2)) = -4 / 6 = -2/3

Since both lines have the same slope, they are parallel to each other.