Expand menu menu_open Minimize Start chapters Home History history History expand_more
{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
search
menu_open
{{ courseTrack.displayTitle }}
{{ statistics.percent }}% Sign in to view progress
{{ printedBook.courseTrack.name }} {{ printedBook.name }}
search Use offline Tools apps
Login account_circle menu_open

Writing Equations of Perpendicular Lines

Writing Equations of Perpendicular Lines 1.2 - Solution

arrow_back Return to Writing Equations of Perpendicular Lines

To determine whether the lines are perpendicular, we calculate the product of their slopes. If the product equals -1,\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
AA (0,0)({\color{#0000FF}{0}},{\color{#0000FF}{0}}) & (2,2)({\color{#009600}{2}},{\color{#009600}{2}}) 2020=1\dfrac{{\color{#009600}{2}}-{\color{#0000FF}{0}}}{{\color{#009600}{2}}-{\color{#0000FF}{0}}}=1
BB (0,0)({\color{#0000FF}{0}},{\color{#0000FF}{0}}) & (2,-1)({\color{#009600}{2}},{\color{#009600}{\text{-}1}}) -1020=-0.5\dfrac{{\color{#009600}{\text{-}1}}-{\color{#0000FF}{0}}}{{\color{#009600}{2}}-{\color{#0000FF}{0}}}=\text{-}0.5
CC (0,3)({\color{#0000FF}{0}},{\color{#0000FF}{3}}) & (-2,-1)({\color{#009600}{\text{-}2}},{\color{#009600}{\text{-}1}}) -13-20=2\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 -1.\text{-}1.

Lines Slope 1 Slope 2 Product
AA & BB 11 -0.5\text{-}0.5 -0.5\text{-}0.5
AA & CC 11 22 22
BB & CC -0.5\text{-}0.5 22 -1\text{-}1

The lines BB and CC are perpendicular.