MATH PROBLEM FIRST TO ANSWER

Question

Let d be the (shortest) distance between 2 parallel lines with slope 6 whose x-intercepts are 8 units apart. Find d^2.

Answer 1

First line :

Slope m = 6

let x-intercepts = 1. So point is ( 1 , 0 )

Slope intercept form : y = mx + c₁

Substitute point( 1 , 0 ) and m = 6

0 = (6)(1) + c₁

c₁ = -6

y = 6x - 6

Second line :

Slope m = 6

parallel lines are 8 units apart

x-intercepts = 1+8 = 9. So point is ( 9 , 0 )

Slope intercept form : y = mx + c₂

Substitute point( 9 , 0 ) and m = 6

0 = (6)(9) + c₂

c₂ = -54

y = 6x - 54

Distance between two parallel lines is :d = |c₂-c₁|/√(1+m²)

d = |-54-(-6)|/√(1+6²)

d = 48/√(37)

d = 7.89 units

Square on both sides

d² = 7.89²

d² = 62.27

Solution :

Distance between two parallel lines is d = 7.89 units

d² = 62.27