IB Maths AA 3.1 Notes

This page contains our IB Maths AA notes for 3.1. By reading each one of these notes, you will fully cover the content for IB Maths AA '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: Unit Circle 3.6: Trigonometric Identities 3.7: Trigonometric Graphs (HL)3.8: Advanced trigonometry (HL)3.9: Compound angles (HL)3.10: Vectors (HL)3.11: Lines (HL)3.12: Planes

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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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