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IBMathsDPApplications & Interpretation (AI)HLRevision Notes3. Geometry & TrigonometryGeometry ToolkitPerpendicular Bisectors

Perpendicular Bisectors (DP IB Applications & Interpretation (AI)): Revision Note

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DP Applications & Interpretation (AI): HLDP Applications & Interpretation (AI): SL

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Perpendicular Bisectors

What is a perpendicular bisector?

  • A perpendicular bisector of a line segment is a line that

    • is perpendicular to the line segment

    • cuts the line segment into two equal halves

  • The perpendicular bisector goes through the midpoint of the line segment

How do I find the equation of the perpendicular bisector of a line segment?

  • STEP 1
    Find the coordinates of the midpoint of the line segment

    • Use the formula open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction comma space fraction numerator y subscript 1 plus y subscript 2 over denominator 2 end fraction close parentheses

  • STEP 2
    Find the gradient of the line segment

    • Use the formula m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction

  • STEP 3
    Find the gradient of the perpendicular bisector

    • Use the formula m subscript perpendicular equals negative 1 over m

  • STEP 4
    Find the equation of the straight line using the gradient and midpoint

    • Use the formula y minus blank y subscript 1 equals m space left parenthesis x minus blank x subscript 1 right parenthesis

  • STEP 5
    Rearrange into the required form

    • Either y equals m x plus c  or  a x plus b y plus d equals 0 

    • These equations for a straight line are given in the formula booklet

Worked Example

Point straight A has coordinates left parenthesis 4 comma space minus 6 right parenthesis and point straight B has coordinates left parenthesis 8 comma space 6 right parenthesis.  Find the equation of the perpendicular bisector to open square brackets AB close square brackets.

Give your answer in the form a x plus b y plus d equals 0.

ai-sl-3-1-1-perp-bis-we

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    Amber

    Author: Amber

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    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.