Perpendicular lines
Introduction
The angle of intersection of two mutually perpendicular lines is 90 degrees. There is a mathematical relation between the gradients of perpendicular lines. Press "newline" to views another example perpendicular lines. Can you figure out a relation between the gradient of the blue line and the red line?
This is relation you should have discovered: when the blue line has a gradient m, the perpendicular red line line will then have gradient a -1/m. It is useful to consider m as a fraction, where a and b are integers:
Parallel Line Though a Given Point
Determine the equation of the straight line that is perpendicular to the blue line and passes through the red point? The required line is the pulsating orange line.
The equation of the line can be found algebraically as follows:
Exercise: Find equation of the perpendicular Line.
Given the line and point:
Find the line which is perpendicular to the above line and passes through the point. Show your working out on paper and don't use a calculator.
numerator
denominator
numerator
denominator
Check your working out below:
Summary
(1) Line with gradient m and -1/m are mutually perpendicular.
(2) For a line with a specified gradient that passes through a given point; the c value can be found by substituting the x and y values from the coordinate in the equation of the line.