# Finding Distance and Midpoint

## Key Questions

• $D = \sqrt{{\left({P}_{{1}_{x}} - {P}_{{2}_{x}}\right)}^{2} + {\left({P}_{{1}_{y}} - {P}_{{2}_{y}}\right)}^{2} + {\left({P}_{{1}_{z}} - {P}_{{2}_{z}}\right)}^{2}}$

What is the distance between M(7,−1,5) and the origin?

• We live in 3 dimensions.

We have East/West, North/South and Up/Down.

If something is 100 m East, and 120 m North and 80 m Above me, then the distance between us is a distance in 3 dimensions, And the middle of that distance is the midpoint.

• The answer is $M = \left(\frac{{P}_{{1}_{x}} + {P}_{{2}_{x}}}{2} , \frac{{P}_{{1}_{y}} + {P}_{{2}_{y}}}{2} , \frac{{P}_{{1}_{z}} + {P}_{{2}_{z}}}{2}\right)$.

The midpoint is one of the easier things to calculate. Remember that mid is a synonym for average. To find the midpoint, we just average the components.