# Arithmetic Mean of a and b

#### rapture

Show that the arithmetic mean of a and b is equidistant from a and b.

#### JeffM

What is the formula for distance?

What is the formula for arithmetic mean?

• 1 person

#### rapture

In what way can I use the two formulas you hinted about
to show my proof?

#### JeffM

In what way can I use the two formulas you hinted about
to show my proof?
Try this. USING THE FORMULAS, WRITE DOWN the distance between a and the arithmetic mean. What is it? Write down the distance between b and the arithmetic mean. What is it? Do you see any way to equate those two expressions?

If you do not see a way to equate them, please post your answers to the distance questions, and say what you tried. I'll bet big money you can solve this on your own after you write down the distances.

Many students think that you find the answer before writing anything down. Not at all. You START by writing down what you know, all of it, and look for connections.

• 1 person

#### Plato

MHF Helper
In what way can I use the two formulas you hinted about
to show my proof?
Given that each of $p~\&~q$ is a real number the by definition $|p-q|=|q-p|$ is the distance from $q$ to $p$.

Show that $\left|a-\dfrac{a+b}{2}\right |=\left|b-\dfrac{a+b}{2}\right |$

• 1 person