Line ℓ1 has the equation x+y=1 and line ℓ2 has the equation x+y= – 3. Find the distance between ℓ1 and ℓ2

Answer 1

This is parallel lines. Let take some point on l₁ is (1, 0). Distance from this point to second line y = - x - 3.

Slope of perpendicular line m = 1 and equation is y = 0 + 1(x - 1) or y = x -1.

From system y = - x - 3 and y = x - 1 we get intersection point: y = - 2 and x = - 1 or (-1, - 2).

Distance from (1, 0) and (- 1, - 2) and will be distance between these parallel lines, d = √2² + 2² = 2√2