3D Coordinate Geometry (DP IB Analysis & Approaches (AA): SL): Revision Note

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 $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ are $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2}\right)$

  • It is just the average of the two coordinates

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 $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ is $d=\sqrt{{\left(x_1-x_2\right)}^2+{\left(y_1-y_2\right)}^2+{\left(z_1-z_2\right)}^2}$

  • This is just an application of Pythagoras' Theorem