IB Maths AI Topic 3 Notes

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:

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

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 $3\sqrt{6}$.