Question

find each length.
a -3 -2 b -1 c 0 d 1 e 2 3
ab =
ad =
be =
ae =

Explanation:

Step1: Recall distance formula on number - line

The distance between two points \(x_1\) and \(x_2\) on a number - line is \(d=\vert x_2 - x_1\vert\).

Step2: Calculate \(AB\)

Point \(A=-3\) and point \(B = - 1\). Then \(AB=\vert-1-(-3)\vert=\vert-1 + 3\vert=\vert2\vert = 2\).

Step3: Calculate \(AD\)

Point \(A=-3\) and point \(D = 1\). Then \(AD=\vert1-(-3)\vert=\vert1 + 3\vert=\vert4\vert = 4\).

Step4: Calculate \(BE\)

Point \(B=-1\) and point \(E = 3\). Then \(BE=\vert3-(-1)\vert=\vert3 + 1\vert=\vert4\vert = 4\).

Step5: Calculate \(AE\)

Point \(A=-3\) and point \(E = 3\). Then \(AE=\vert3-(-3)\vert=\vert3 + 3\vert=\vert6\vert = 6\).

Answer:

\(AB = 2\)
\(AD = 4\)
\(BE = 4\)
\(AE = 6\)