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

The distance formula is \[d=\sqrt{(x _{2}-x _{1})^{2}+(y _{2}-y _{1})^{2}}\]Since the two points are on the x-axis, y2-y1=0

So the equation reduces to this:

\[d=\sqrt{(x _{2}-x _{1})^{2}}\] Let x2 = a and x1=b\[d=\sqrt{(a-b)^{2}}\]\[d ^{2}=(a-b)^{2}\]Since \[\left| c \right|=c ^{2}\] then\[(a-b)^{2}=\left| a-b \right|\]