Perpendicular lines exist at right angles to each other.
Two perpendicular lines are shown on the graph below. The line of one graph is given by y = 2x + 2, and the other by y = -`frac(1)(2)`x + 3.
Lines are perpendicular if the gradients of the two lines multiplied together = -1.
1. What is the equation of the line that is perpendicular to y = 3x -3 that also passes through (0, 5)?
Answer: y = -`frac(1)(3)`x + 5
The gradient of the original line is 3. The gradient of the perpendicular line = - `frac(1)(3)` (reciprocal of the original gradient x -1).
The intercept of the line is given by the fact that it passes through (0, 5).
2. Find the equation of the line perpendicular to y = `frac(1)(2)`x - 3 that passes through (4, 4).
Answer: y = -2x + 12
The gradient of the second line is given by - 1 / `frac(1)(2)` = -2.
The lines passes through the point (4, 4): 4 = -2 x 4 + c, where c is the intercept = 12.
The equation of the line is y = -2x + 12.