Perpendicular lines
Identify and construct perpendicular lines in Grade 10 geometry using the negative reciprocal slope rule, where the product of their slopes equals -1.
Key Concepts
Perpendicular lines have slopes that are negative reciprocals of each other. The product of the slopes of two perpendicular lines is $ 1$. $$m 1 m 2 = 1$$.
A line with slope $m 1 = 4$ is perpendicular to a line with slope $m 2 = \frac{1}{4}$, because $4( \frac{1}{4}) = 1$. To find the perpendicular slope for $m = \frac{2}{3}$, flip the fraction and change the sign to get $m = \frac{3}{2}$.
Perpendicular lines are like the corners of a perfect square, meeting at a crisp 90 degree angle. Their slopes are total opposites! To get one from the other, you flip the fraction (that's the reciprocal part) and switch its sign. When you multiply these opposite reciprocal slopes together, they always cancel out to make exactly $ 1$, proving their perpendicularity.
Common Questions
How do you identify perpendicular lines from their equations?
Find the slopes of both lines. If their product equals -1, the lines are perpendicular. For example, slopes 2 and -1/2 multiply to give -1.
What is the slope of a line perpendicular to y = 4x - 3?
The slope of the given line is 4. The perpendicular slope is the negative reciprocal: -1/4.
Are vertical and horizontal lines perpendicular to each other?
Yes. A vertical line has undefined slope and a horizontal line has slope 0. They form a 90° angle, making them perpendicular, even though the slope rule does not directly apply.