Question

Line ℓ1 has the equation y=x–5 and line ℓ2 has the equation y=x–1. Find the distance between ℓ1 and ℓ2. round your answer to the nearest tenth

Answer 1

$\ell_1$ and $\ell_2$ are parallel to one another with slope 1. Any line with slope -1 is perpendicular to both of these lines, the simplest being $y=-x$.

This perpendicular line intersects $\ell_1$ and $\ell_2$ at the points (5/2, -5/2) and (1/2, -1/2), respectively.

The distance between $\ell_1$ and $\ell_2$ is the same as the distance between these two intersections:

$\sqrt{\left(\dfrac52-\dfrac12\right)^2+\left(-\dfrac52+\dfrac12\right)^2}=2\sqrt2\approx\boxed{2.8}$