Revision NotesExam QuestionsFlashcardsPast PapersMock Exams
IBMathsDPApplications & Interpretation (AI)HLRevision Notes3. Geometry & TrigonometryGeometry of 3D Shapes3D Coordinate Geometry

3D Coordinate Geometry (DP IB Applications & Interpretation (AI)): Revision Note

Amber

Written by: Amber

Reviewed by: Dan Finlay

Updated on

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

Did this video help you?

3D Coordinate Geometry

How do I find the midpoint of two points in 3D?

  • The midpoint of two points is the middle point

    • It lies on the line segment joining the two points together

    • It is the point that is equidistant from the two points

  • The coordinates of the midpoint of open parentheses x subscript 1 comma space y subscript 1 comma space z subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 comma space z subscript 2 close parentheses are 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 comma space fraction numerator z subscript 1 plus z subscript 2 over denominator 2 end fraction close parentheses

    • It is just the average of the two coordinates

Examiner Tips and Tricks

This is given in the formula booklet under the geometry and trigonometry section.

How do I find the distance between two points in 3D?

  • The distance between two points is the length of the line segment joining them

  • The length of the line segment between open parentheses x subscript 1 comma space y subscript 1 comma space z subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 comma space z subscript 2 close parentheses is d equals square root of open parentheses x subscript 1 minus x subscript 2 close parentheses squared plus open parentheses y subscript 1 minus y subscript 2 close parentheses squared plus open parentheses z subscript 1 minus z subscript 2 close parentheses squared end root

    • This is just an application of Pythagoras' Theorem

Examiner Tips and Tricks

This is given in the formula booklet under the geometry and trigonometry section.

Worked Example

The points straight A and straight B  have coordinates left parenthesis negative 2 comma space 1 comma space 5 right parenthesis and left parenthesis 4 comma space minus 3 comma space 2 right parenthesis respectively.

i) Calculate the distance of the line segment AB.

3-2-1-ai-sl-3d-coord-geo-we-solution-i

ii) Find the midpoint of open square brackets AB close square brackets.

3-2-1-ai-sl-3d-coord-geo-we-solution-ii

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 yourselfFlashcards

    Did this page help you?

    Previous:Arcs & Sectors Using RadiansNext:Volume & Surface Area
    Author
    Reviewer
    Amber

    Author: Amber

    Expertise: Maths Content Creator

    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.

    Dan Finlay

    Reviewer: 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.

    OSZAR »