Question

use this diagram for the following:
find each measure:
cg dg ab cb
de gh eh ah
ac ch fb cd

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: Find \(CG\)

Let \(C=- 5\) and \(G = 4\). Then \(CG=\vert4-(-5)\vert=\vert4 + 5\vert = 9\).

Step3: Find \(DG\)

Let \(D=-2\) and \(G = 4\). Then \(DG=\vert4-(-2)\vert=\vert4 + 2\vert=6\).

Step4: Find \(AB\)

Let \(A=-7\) and \(B = 2\). Then \(AB=\vert2-(-7)\vert=\vert2 + 7\vert = 9\).

Step5: Find \(CB\)

Let \(C=-5\) and \(B = 2\). Then \(CB=\vert2-(-5)\vert=\vert2 + 5\vert = 7\).

Step6: Find \(DE\)

Let \(D=-2\) and \(E = 0\). Then \(DE=\vert0-(-2)\vert=\vert0 + 2\vert = 2\).

Step7: Find \(GH\)

Let \(G = 4\) and \(H = 7\). Then \(GH=\vert7 - 4\vert=3\).

Step8: Find \(EH\)

Let \(E = 0\) and \(H = 7\). Then \(EH=\vert7-0\vert = 7\).

Step9: Find \(AH\)

Let \(A=-7\) and \(H = 7\). Then \(AH=\vert7-(-7)\vert=\vert7 + 7\vert = 14\).

Step10: Find \(AC\)

Let \(A=-7\) and \(C=-5\). Then \(AC=\vert-5-(-7)\vert=\vert-5 + 7\vert = 2\).

Step11: Find \(CH\)

Let \(C=-5\) and \(H = 7\). Then \(CH=\vert7-(-5)\vert=\vert7 + 5\vert = 12\).

Step12: Find \(FB\)

Let \(F = 1\) and \(B = 2\). Then \(FB=\vert2 - 1\vert=1\).

Step13: Find \(CD\)

Let \(C=-5\) and \(D=-2\). Then \(CD=\vert-2-(-5)\vert=\vert-2 + 5\vert = 3\).

Answer:

\(CG = 9\), \(DG = 6\), \(AB = 9\), \(CB = 7\), \(DE = 2\), \(GH = 3\), \(EH = 7\), \(AH = 14\), \(AC = 2\), \(CH = 12\), \(FB = 1\), \(CD = 3\)