Question

Determine whether the lines passing through the pairs of points are parallel, perpendicular or neither. Line a: (−4,4) and (8,−10) Line b: (4,8) and (18,20)

Answer 1

Answer:

Perpendicular.

Step-by-step explanation:

Find the slopes of each line through $m = \frac{(y_2-y_1)}{(x_2-x_1 )}$

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.