The distance between the lines y = 2x + 3 and y = 2x + 4 is

Question

Question

Answer 1

Concept:

Distance between two parallel lines:

The distance d between two parallel lines y = mx + c₁ and y = mx + c₂ is given by d = \(\rm \frac{\left | c_{2} - c_{1} \right |}{\sqrt{1 + m^{2}}}\)

Calculation:

Given equation of lines are y = 2x + 3 and y = 2x + 4

Perpendicular distance = \(\rm \frac{\left | 4 - 3 \right |}{\sqrt{1 + 2^{2}}}\) = \(\rm \frac{1}{\sqrt{5}}\)

The distance between the lines y = 2x + 3 and y = 2x + 4 is \(\rm \frac{1}{\sqrt{5}}\)