Distance between Parallel Lines

Question

Find the distance between the pair of parallel lines; y = 2x + 4 and y = 2x – 2.

a. 2.68

b. 2.75

c. 2.94

d. 3.11

Answer 1

y = 2x + 4

y = 2x - 2

express in form ax + by + c = 0

2x - y - 4 = 0

2x - y + 2 = 0

A = 2, B = 1, C2 = 2, C1 = -4

d = abs ((C2 - C1)/sqrt(A^2 + B^2)) = 6/sqrt(5) = 2.68

Answer 2

Draw and label a diagram!

Distance is measured on the normal (perpendicular) to the lines.

The normal to the first equation passing through the same y-intercept is

y = -0.5x + 4

This normal intersects the second line when

-0.5x + 4 = 2x - 2

6 = 2.5x2.8

2.4 = x, or at (2.4, 2.8))

The normal is from (0, 4) to (2.4, 2.8)

Use the distance formula to determine the distance tween the two points