2. Parallel Lines

Distance Between Lines — Quiz

Test your understanding of distance between lines with 5 practice questions.

Practice Questions

Question 1

Given two parallel lines, $L_1$ with equation $5x + 12y - 13 = 0$ and $L_2$ with equation $5x + 12y + 26 = 0$. What is the perpendicular distance between these two lines?

Question 2

A point $P(x, y)$ is equidistant from the line $y = 3$ and the line $x = -1$. Which of the following equations represents the locus of point $P$?

Question 3

Consider a line $L$ with the equation $y = \frac{3}{4}x - 2$. A point $Q(8, 1)$ is given. What is the equation of the line perpendicular to $L$ that passes through $Q$?

Question 4

A rectangle has vertices at $(0, 0)$, $(6, 0)$, $(6, 4)$, and $(0, 4)$. What is the distance from the center of the rectangle to its longest side?

Question 5

The distance between the parallel lines $y = mx + c_1$ and $y = mx + c_2$ is given by $d = \frac{|c_1 - c_2|}{\sqrt{m^2 + 1}}$. If the distance between $y = 2x + 10$ and $y = 2x - 5$ is $d$, what is the value of $d^2$?