Question

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.

Answer 1

@phi

Answer 2

@mathlover2014 @Jhannybean

Answer 3

@HelloKitty17 @They_Call_Me_Narii @FEARLESS_JOCEY

Answer 4

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

Answer 5

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

Answer 6

Are you there? Lol

Answer 7

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)

Answer 8

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 ?

Answer 9

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

Answer 10

just use letters instead of numbers.

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

the square root of that

Answer 18

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

Answer 19

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

Answer 20

Ok is that all?

Answer 21

yes

Answer 22

Thank you!!