Geometry Question. Will give medal to whoever can give me a good answer. Thanks
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

mustap · Answer

If anyone can help me that would be helpful. I have a small idea of what to do, but this question seems to confuse me for some reason.

mustap · Answer

@Saisuke<3 do you think you could help? you've been watching for a while now

anonymous · Answer

OH sorry!!!! i looked at the question but idk how to help u! im so so so sorry!!!! :(

mustap · Answer

oh thats fine I was just expecting you to start writing any second. Thanks anyways

mustap · Answer

@jim_thompson5910 
@iambatman @SolomonZelman @pooja195 
would appreciate some help from any one of you guys

jim_thompson5910 · Answer

EVERY point on the x axis is of the form (x,0) where x is some number

examples: 
(3,0)
(2,0)
(9,0)
(27,0)
etc

jim_thompson5910 · Answer

The distance formula is 

$$\Large d = \sqrt{\left(x_{2}-x_{1}\right)^2+\left(y_{2}-y_{1}\right)^2}$$

so you plug in the two points (a,0) and (b,0) into this formula above

mustap · Answer

so would it be
$$d=\sqrt{(b-a)^2(0-0)^2}$$

mustap · Answer

how should I write this as the final answer? I'm pretty sure there has to be more to it.

jim_thompson5910 · Answer

$$\Large d = \sqrt{\left(x_{2}-x_{1}\right)^2+\left(y_{2}-y_{1}\right)^2}$$
$$\Large d = \sqrt{\left(a-b\right)^2+\left(0-0\right)^2}$$
$$\Large d = \sqrt{\left(a-b\right)^2+\left(0\right)^2}$$
$$\Large d = \sqrt{\left(a-b\right)^2+0}$$
$$\Large d = \sqrt{\left(a-b\right)^2}$$
$$\Large d = |a-b|$$


Note: $\Large |a-b| = |b-a|$ so order does not matter in this particular case

jim_thompson5910 · Answer

you forgot the + in between the parenthesis

mustap · Answer

oh yeah I forgot the plus.

jim_thompson5910 · Answer

btw this trick works for any horizontal or vertical line. It doesn't have to be the x axis

mustap · Answer

so I just have to solve for d in the formula?

jim_thompson5910 · Answer

it says "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."

and the steps are given above. So that's all you need to do really

mustap · Answer

I thought the question was more complicated then that

mustap · Answer

okay thanks alot!

jim_thompson5910 · Answer

np