Question

use the number line to find the length. length of the line segments 1) a) cb = b) ad+fb = c) ed = 40 units d) ef - af = e) ca = f) ab = 2) a) ps+rq = b) sq = c) pq - rt = d) st = e) rt = 3) a) jn = b) lm+nk = c) lk = d) jn - lm =

Explanation:

Step1: Recall length - finding formula on number line

The length of a line - segment with endpoints \(a\) and \(b\) on a number line is \(|a - b|\).

Step2: Solve part 1a

For \(CB\), if \(C=-16\) and \(B = 24\), then \(CB=|24-(-16)|=|24 + 16| = 40\).

Step3: Solve part 1b

For \(AD+FB\), if \(A = 4\), \(D = 8\), \(F = 12\), \(B = 24\). Then \(AD=|8 - 4|=4\) and \(FB=|24 - 12| = 12\), so \(AD + FB=4+12 = 16\).

Step4: Solve part 1c

For \(ED\), if \(E=-8\) and \(D = 8\), then \(ED=|8-(-8)|=|8 + 8| = 16\).

Step5: Solve part 1d

For \(EF - AF\), if \(E=-8\), \(F = 12\), \(A = 4\). Then \(EF=|12-(-8)|=20\) and \(AF=|12 - 4| = 8\), so \(EF - AF=20 - 8=12\).

Step6: Solve part 1e

For \(CA\), if \(C=-16\) and \(A = 4\), then \(CA=|4-(-16)|=|4 + 16| = 20\).

Step7: Solve part 1f

For \(AB\), if \(A = 4\) and \(B = 24\), then \(AB=|24 - 4| = 20\).

Step8: Solve part 2a

For \(PS+RQ\), if \(P = 12\), \(S = 18\), \(R = 36\), \(Q = 72\). Then \(PS=|18 - 12| = 6\) and \(RQ=|72 - 36| = 36\), so \(PS+RQ=6+36 = 42\).

Step9: Solve part 2b

For \(SQ\), if \(S = 18\) and \(Q = 72\), then \(SQ=|72 - 18| = 54\).

Step10: Solve part 2c

For \(PQ - RT\), if \(P = 12\), \(Q = 72\), \(R = 36\), \(T = 48\). Then \(PQ=|72 - 12| = 60\) and \(RT=|48 - 36| = 12\), so \(PQ - RT=60 - 12 = 48\).

Step11: Solve part 2d

For \(ST\), if \(S = 18\) and \(T = 48\), then \(ST=|48 - 18| = 30\).

Step12: Solve part 2e

For \(RT\), if \(R = 36\) and \(T = 48\), then \(RT=|48 - 36| = 12\).

Step13: Solve part 3a

For \(JN\), if \(J=-33\) and \(N=-12\), then \(JN=|-12-(-33)|=|-12 + 33| = 21\).

Step14: Solve part 3b

For \(LM+NK\), if \(L=-24\), \(M=-15\), \(N=-12\), \(K = 0\). Then \(LM=|-15-(-24)|=9\) and \(NK=|0-(-12)| = 12\), so \(LM+NK=9 + 12=21\).

Step15: Solve part 3c

For \(LK\), if \(L=-24\) and \(K = 0\), then \(LK=|0-(-24)| = 24\).

Step16: Solve part 3d

For \(JN - LM\), if \(J=-33\), \(N=-12\), \(L=-24\), \(M=-15\). Then \(JN=21\) and \(LM = 9\), so \(JN - LM=21 - 9 = 12\).

Answer:

1a. \(40\)
1b. \(16\)
1c. \(16\)
1d. \(12\)
1e. \(20\)
1f. \(20\)
2a. \(42\)
2b. \(54\)
2c. \(48\)
2d. \(30\)
2e. \(12\)
3a. \(21\)
3b. \(21\)
3c. \(24\)
3d. \(12\)