Question

P(-3, 1) and Q (-7, -2); R(2, -1) and S (8,4); m = (y2 - y1) / (x2 - x1); determine if it is parallel or perpendicular.

A. The lines are parallel.
B. The lines are perpendicular.
C. The lines neither parallel nor perpendicular.
D. Not enough information to determine.

Answer 1

To determine if the lines represented by the given points are parallel or perpendicular, calculate their slopes using the formula m = (y2 - y1) / (x2 - x1). If the slopes are equal, the lines are parallel. If the slopes are negative reciprocals, the lines are perpendicular. If neither condition is met, the lines are neither parallel nor perpendicular.

Step-by-step explanation:

To determine if the lines represented by the points P(-3, 1) and Q(-7, -2) and the points R(2, -1) and S(8, 4) are parallel or perpendicular, we need to first calculate the slopes of the lines.

The slope of a line can be calculated using the formula m = (y2 - y1) / (x2 - x1).

1. For the line represented by P and Q: m1 = (-2 - 1)/(-7 - (-3)) = -3/(-4) = 3/4
2. For the line represented by R and S: m2 = (4 - (-1))/(8 - 2) = 5/6

Since the slopes of the two lines are not equal and they do not have negative reciprocal slopes, the lines are neither parallel nor perpendicular to each other. Therefore, the correct answer is C. The lines are neither parallel nor perpendicular.