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

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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

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