Use the Distance Formula and the x-axis of the coordinate plane. Show why the distance between two points on a number line (the x-axis) is | a – b |, where a and b are the x-coordinates of the points.

Question

anonymous · Answer

okay, so do you know what the distance formula is?

anonymous · Answer

Since we know the points are on the $x$ axis, then their $y$-coordinates must be $0$.

anonymous · Answer

So we need to show the distance between $(a,0)$ and $(b,0)$ equals $|a-b|$.

anonymous · Answer

Yes, I'm just not entirely sure how to do that

anonymous · Answer

Okay, what is the distance formula?

anonymous · Answer

The distance between the given points?

anonymous · Answer

I mean, do you know the formula for finding the distance between two points?

anonymous · Answer

No, that's what I need help with.

anonymous · Answer

Okay, if you have two points $(x_1,y_1)$ and $(x_2,y_2)$ then the distance between them is given by: $$
|(x_1,y_1)(x_2,y_2)|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
$$

anonymous · Answer

In our case, we end up with: $$
\sqrt{(b-a)^2+(0-0)^2}
$$

anonymous · Answer

Can you simplify this?

anonymous · Answer

b-a?

anonymous · Answer

Can you show your work?

anonymous · Answer

$$
x_2=b\quad\text{and}\quad x_1=a
$$