Perpendicular Lines Flashcards

All 6 cards in this deck

What is the product of the gradients of two perpendicular lines?

$-1$, i.e. $m_1 m_2 = -1$.

What is the gradient of a line perpendicular to a line of gradient $m$?
e.g. $m = \frac{3}{2}$

The negative reciprocal, $-\frac{1}{m}$.
e.g. $-\frac{2}{3}$

What are the steps to find the equation of the line perpendicular to a given line through a given point?
e.g. perpendicular to $y = 3x - 4$ through $(9, 5)$

1. Negative reciprocal of the gradient: $-\frac{1}{3}$
2. Substitute the point into $y = -\frac{1}{3}x + c$: $5 = -3 + c$, so $c = 8$
3. Equation: $y = -\frac{1}{3}x + 8$

True or false? A line perpendicular to $y = 2x + 1$ has gradient $-2$.

False. The gradient is $-\frac{1}{2}$, the negative reciprocal of $2$.

True or false? $y = -\frac{1}{2}x + 3$ and $y = 2x - 1$ are perpendicular.

True. $-\frac{1}{2} \times 2 = -1$.

What is the equation of a line perpendicular to the horizontal line $y = 4$?

A vertical line $x = a$ for some number $a$, e.g. $x = 2$.