Practice Perpendicularity in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Lines, segments, or planes that intersect at exactly a right angle of 90° to each other.
The corner of a book or a room—the two edges meet at precisely 90°.
Example 1
easyLine \ell_1: y = 2x + 1. Write the equation of a line \ell_2 perpendicular to \ell_1 that passes through (4, 3).
Example 2
mediumDetermine whether triangle A(0,0), B(4,0), C(4,3) is a right triangle, and if so identify the right angle vertex.
Example 3
easyLine m passes through (0, -1) with slope \dfrac{3}{5}. Write the equation of the line perpendicular to m through the origin.
Example 4
hardFind the foot of the perpendicular from point P(3, 7) to the line \ell: y = 2x - 1.