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Writing Equations of Perpendicular Lines

Writing Equations of Perpendicular Lines 1.2 - Solution

To determine whether the lines are perpendicular, we calculate the product of their slopes. If the product equals $\text{-} 1,$ then the lines are perpendicular. Thus, we need to find the slopes of the lines. For that, we need two points on each line.

We can now use the points to calculate the slope using the slope formula.

Line Points Slope
$A$ $({\color{#0000FF}{0}},{\color{#0000FF}{0}})$ & $({\color{#009600}{2}},{\color{#009600}{2}})$ $\dfrac{{\color{#009600}{2}}-{\color{#0000FF}{0}}}{{\color{#009600}{2}}-{\color{#0000FF}{0}}}=1$
$B$ $({\color{#0000FF}{0}},{\color{#0000FF}{0}})$ & $({\color{#009600}{2}},{\color{#009600}{\text{-}1}})$ $\dfrac{{\color{#009600}{\text{-}1}}-{\color{#0000FF}{0}}}{{\color{#009600}{2}}-{\color{#0000FF}{0}}}=\text{-}0.5$
$C$ $({\color{#0000FF}{0}},{\color{#0000FF}{3}})$ & $({\color{#009600}{\text{-}2}},{\color{#009600}{\text{-}1}})$ $\dfrac{{\color{#009600}{\text{-}1}}-{\color{#0000FF}{3}}}{{\color{#0000FF}{\text{-}2}}-{\color{#0000FF}{0}}}=2$

To determine if the lines are perpendicular or not we should multiply their slopes and see if it equals $\text{-}1.$

Lines Slope 1 Slope 2 Product
$A$ & $B$ $1$ $\text{-}0.5$ $\text{-}0.5$
$A$ & $C$ $1$ $2$ $2$
$B$ & $C$ $\text{-}0.5$ $2$ $\text{-}1$

The lines $B$ and $C$ are perpendicular.