Revision NotesExam QuestionsFlashcardsPast PapersMock Exams
IBMathsDPAnalysis & Approaches (AA)SLRevision Notes2. FunctionsLinear Functions & GraphsParallel & Perpendicular Lines

Parallel & Perpendicular Lines (DP IB Analysis & Approaches (AA)): Revision Note

Dan Finlay

Last updated

DP Analysis & Approaches (AA): SLDP Analysis & Approaches (AA): HLDP Applications & Interpretation (AI): HLDP Applications & Interpretation (AI): SLDP Applications & Interpretation (AI): HLDP Applications & Interpretation (AI): SLDP Analysis & Approaches (AA): HLDP Analysis & Approaches (AA): SL

Did this video help you?

Parallel Lines

How are the equations of parallel lines connected?

  • Parallel lines are always equidistant meaning they never intersect

  • Parallel lines have the same gradient

    • If the gradient of line l1 is m1 and gradient of line l2 is m2 then...

      • m subscript 1 equals m subscript 2 rightwards double arrow l subscript 1 blank & blank l subscript 2 blank are blank parallel

      • l subscript 1 blank & blank l subscript 2 blank are blank parallel rightwards double arrow m subscript 1 equals m subscript 2

  • To determine if two lines are parallel:

    • Rearrange into the gradient-intercept form space y equals m x plus c

    • Compare the coefficients of space x

    • If they are equal then the lines are parallel

Parallel & Perpendicular Gradients Notes Diagram 1

Worked Example

The line space l  passes through the point space left parenthesis 4 comma negative 1 right parenthesis  and is parallel to the line with equation space 2 x minus 5 y equals 3 .

Find the equation of space l , giving your answer in the form space y equals m x plus c.

2-1-1-ib-ai-sl-parallel-lines-we-solution

 

Did this video help you?

Perpendicular Lines

How are the equations of perpendicular lines connected?

  • Perpendicular lines intersect at right angles

  • The gradients of two perpendicular lines are negative reciprocals

    • If the gradient of line l1 is m1 and gradient of line l2 is m2 then...

      • space m subscript 1 cross times m subscript 2 equals negative 1 space rightwards double arrow space l subscript 1 space & space l subscript 2 space are space perpendicular

      •   l subscript 1 space & space l subscript 2 space are space perpendicular space rightwards double arrow space m subscript 1 cross times m subscript 2 equals negative 1

  • To determine if two lines are perpendicular:

    • Rearrange into the gradient-intercept form space y equals m x plus c

    • Compare the coefficients of space x

    • If their product is -1 then they are perpendicular

  • Be careful with horizontal and vertical lines

    • space x equals p and space y equals q are perpendicular where p and q are constants

Parallel & Perpendicular Gradients Notes Diagram 3

Worked Example

The line space l subscript 1  is given by the equation space 3 x minus 5 y equals 7.

The line space l subscript 2  is given by the equation space y equals 1 fourth minus 5 over 3 x .

Determine whether space l subscript 1 and space l subscript 2 are perpendicular. Give a reason for your answer.

2-1-1-ib-ai-sl-perpendicular-lines-we-solution

You've read 0 of your 5 free revision notes this week

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

    Test yourself

    Did this page help you?

    Previous:Equations of a Straight LineNext:Quadratic Functions
    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Subject Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.