IB Maths AI 3.1 Notes

This page contains our IB Maths AI notes for 3.1. By reading each one of these notes, you will fully cover the content for IB Maths AI 'Fundamentals of geometry'.

All Topic 3 Sub-topics 3.1: Fundamentals Of Geometry 3.2: Introduction To Trigonometry 3.3: Applied Trigonometry 3.4: Circles 3.5: Perpendicular Bisectors 3.6: Voronoi Diagrams (HL)3.7: Unit circle (HL)3.8: Geometric transformations (HL)3.9: Vectors (HL)3.10: Vector lines (HL)3.11: Graph theory (HL)3.12: Adjacency matrices (HL)3.13: Algorithms & problems

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Chapters

1. Distance in 3D

2. Midpoint in 3D

3. Volume of 3D solids

4. Surface area of 3D solids

5. Angles in 3D shapes

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Distance in 3D

If two points are $A(x_1,y_1,z_1)$ and $B(x_2,y_2,z_2)$ , then the distance between them is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$

Math Topic 3 subTopic 1 notes image 1

This is the three-dimensional version of Pythagoras' theorem.

Find the distance between $A(0,6,0)$ and $D(3,3,6)$ .
Substitute the coordinates into the formula: $d=\sqrt{(3-0)^2+(3-6)^2+(6-0)^2}$ .
$d=\sqrt{3^2+(-3)^2+6^2}$ .
$d=\sqrt{9+9+36}=\sqrt{54}$ .
$d=3\sqrt{6}$ .
So the distance between $A$ and $D$ is $3\sqrt{6}$ .

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