Determine whether the lines through the given pairs of points are parallel. A (1, - 3), B (- 1, - 5) and C (2, 2), D (- 2, 6)
A) The lines through the given pairs of points are not parallel.
B) The lines through the given pairs of points are parallel

Question

Determine whether the lines through the given pairs of points are parallel. A (1, - 3), B (- 1, - 5) and C (2, 2), D (- 2, 6) 
A) The lines through the given pairs of points are not parallel.
B) The lines through the given pairs of points are parallel

Quizplus · Accepted Answer

To determine if the lines through two pairs of points are parallel, we need to find the slopes of the lines. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). If the slopes are equal, the lines are parallel. If the slopes are not equal, the lines are not parallel.

For line AB: slope = (-5 - (-3)) / (-1 - 1) = -2 / -2 = 1
For line CD: slope = (6 - 2) / (-2 - 2) = 4 / -4 = -1

Since the slopes are not equal (-1 ≠ 1), the lines through the given pairs of points are not parallel.

Determine Whether the Lines Through the Given Pairs of Points