Geometry || Distance Formula Question

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.

 

 

I don't really understand it. :l Please explain to me how to do this and how to do future questions like these. Thank you!

Answer 1

distance between two points whose coordinates are x₁y₁ and x₂y₂  ü√(y₂-y₁)² + (x₂-x₁)2

 

In this case a and b are on x axis and their y coordinates are 0. Plug in values x₂ = b and x₁=a

 

Distance = b-a

 

also we know absolute value of b-a is same as that of a-b

:)

Answer 2

On the coordinate plane every point is named by an ordered pair. For points on the x-axis the pair is in the form (x, 0).

 

The two points are (a, 0) and (b, 0). If "d" is the distance between them:

 

d² = (a - b)² + (0 - 0)²

d² = (a - b)²

 

Both sides are positive numbers. Yet a - b need not be a positive number (square a negative get a positive!).

Therefore d = |a - b|.