## Kailee1423 one year ago 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.

1. Kailee1423

@phi

2. Kailee1423

@mathlover2014 @Jhannybean

3. Kailee1423

@HelloKitty17 @They_Call_Me_Narii @FEARLESS_JOCEY

4. phi

Do you know the "distance formula" ? Is it in your notes?

5. Kailee1423

d=the square root of x2-x1^2 + y2-y1^2

6. Kailee1423

Are you there? Lol

7. phi

OS is back. yes that is the correct formula. they want you to use it for two points that lie on the x-axis (that means they y value is 0)

8. phi

for example, the two points can be (a,0) and (b,0) (if we plot them (if we knew what number a and b were) , they would be on the x-axis any way, use the distance formula to find the distance between those two points. can you try to do that ?

9. Kailee1423

I could use the distance formula to find coordinates but this is just explaining without actual coordinates. It's confusing lol

10. phi

just use letters instead of numbers.

11. phi

for example x2 is "b" and x1 is "a" use those letters in the formula the y's are easy: both are 0

12. Kailee1423

So D=(A^2-0^2) + (B^2-0^2) ?

13. phi

I think you mixed x and y together the formula says $D = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

14. Kailee1423

Oh so D=(A^2-B^2) + (0^2-0^2)

15. phi

almost. you don't square each x or y you square the difference. Look at the formula carefully

16. Kailee1423

I see now! Lol It's D=(A-B) + (0-0)

17. Kailee1423

the square root of that

18. phi

it is $D= \sqrt{ (A-B)^2 +(0-0)^2 }$ we can ignore adding zero, so that simplifies to $D= \sqrt{ (A-B)^2}$

19. phi

now we use the definition $|A-B|= \sqrt{(A-B)^2 }$ so show the distance is $D= | A-B|$

20. Kailee1423

Ok is that all?

21. phi

yes

22. Kailee1423

Thank you!!