Question

find the length of the following segments: r g t f u j -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 rt: __________ gt:________ ut:________ tj:________ rf:________ jt:__________

Explanation:

Step1: Recall distance formula

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

Step2: Find length of RT

The coordinate of \(R=-6\) and the coordinate of \(T = - 1\). Then \(RT=\vert-1-(-6)\vert=\vert-1 + 6\vert=\vert5\vert = 5\).

Step3: Find length of GT

The coordinate of \(G=-4\) and the coordinate of \(T=-1\). Then \(GT=\vert-1-(-4)\vert=\vert-1 + 4\vert=\vert3\vert = 3\).

Step4: Find length of UT

The coordinate of \(U = 3\) and the coordinate of \(T=-1\). Then \(UT=\vert3-(-1)\vert=\vert3 + 1\vert=\vert4\vert = 4\).

Step5: Find length of TJ

The coordinate of \(T=-1\) and the coordinate of \(J = 5\). Then \(TJ=\vert5-(-1)\vert=\vert5 + 1\vert=\vert6\vert = 6\).

Step6: Find length of RF

The coordinate of \(R=-6\) and the coordinate of \(F = 2\). Then \(RF=\vert2-(-6)\vert=\vert2 + 6\vert=\vert8\vert = 8\).

Step7: Find length of JT

The coordinate of \(J = 5\) and the coordinate of \(T=-1\). Then \(JT=\vert5-(-1)\vert=\vert5 + 1\vert=\vert6\vert = 6\).

Answer:

RT: 5
GT: 3
UT: 4
TJ: 6
RF: 8
JT: 6