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.

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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.

Mathematics
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  • phi
Do you know the "distance formula" ? Is it in your notes?
d=the square root of x2-x1^2 + y2-y1^2
Are you there? Lol
  • 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)
  • 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 ?
I could use the distance formula to find coordinates but this is just explaining without actual coordinates. It's confusing lol
  • phi
just use letters instead of numbers.
  • phi
for example x2 is "b" and x1 is "a" use those letters in the formula the y's are easy: both are 0
So D=(A^2-0^2) + (B^2-0^2) ?
  • phi
I think you mixed x and y together the formula says \[ D = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\]
Oh so D=(A^2-B^2) + (0^2-0^2)
  • phi
almost. you don't square each x or y you square the difference. Look at the formula carefully
I see now! Lol It's D=(A-B) + (0-0)
the square root of that
  • phi
it is \[ D= \sqrt{ (A-B)^2 +(0-0)^2 } \] we can ignore adding zero, so that simplifies to \[ D= \sqrt{ (A-B)^2}\]
  • phi
now we use the definition \[ |A-B|= \sqrt{(A-B)^2 }\] so show the distance is \[ D= | A-B| \]
Ok is that all?
  • phi
yes
Thank you!!

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