Question

One line passes through the point (-8,1) and (4,4). Another line passes through points (-9,-7) and (9,-3). Are the lines parallel, perpendicular, or neither?

Answer 1

Answer:

The correct answer is neither.

Step-by-step explanation:

To find the relationship between the lines, find the slope of each. You can do this by using the slope formula.

m(slope) = (y2 - y1)/(x2 - x1)

m = (4 - 1)/(4 - -8)

m = 3/12

m = 1/4

Now do so for the second line.

m(slope) = (y2 - y1)/(x2 - x1)

m = (-3 - -7)/(9 - -9)

m = 4/18

m = 2/9

Since they are not the same and not opposite/reciprocal, then we know they are neither parallel nor perpendicular.

Answer 2

Answer: Perpendicular. Step-by-step explanation: Find the slopes of each line through Line a: m = (-10-4) / (8--4) = -14/12 = -7/6 Line b: m = (20-8) / (18 -4) = 12/14 = 6/7 When lines are parallel, they have the same slope. Since -7/2≠6/7, they are not parallel. When lines are perpendicular, the product of the slopes equals -1. -7/6 x 6/7 = -1 The product is -1, hence they are perpendicular lines.