Line ℓ1 has the equation y= - x+1 and line ℓ2 has the equation x+y= - 1. Find the distance between ℓ1 and ℓ2.

Question

Round to the nearest tenth

Answer 1

Let equation 1 be y = -x + 1

Let equation 2 be y = -x - 1 the 2 lines are parallel

Choose a point on equation 1 , one point would be (1,0)

The perpendicular line originating from equation 1 at the point (1,0) would be y_p = x - 1

Now let's see where this line intersects with equation 2 which would be the shortest distance

if x - 1 = -x -1 then 2x = 0 or x = 0 on equation 2. That point would be (0,-1)

The distance between these 2 points is sqrt{ (1-0)2 + (0+1)2) = sqrt(2) = 1.4 (to the nearest tenth)