Question

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

Step1: Find distance between two - points on number line

The length of a line - segment with endpoints \(x_1\) and \(x_2\) on a number line is \(|x_2 - x_1|\).

For 1:

a) \(CB\):

The coordinate of \(C=-16\) and the coordinate of \(B = 24\). So \(CB=|24-(-16)|=|24 + 16| = 40\) units.

b) \(AD+FB\):

The coordinate of \(A = 4\), \(D = 8\), \(F = 12\), \(B = 24\). \(AD=|8 - 4|=4\), \(FB=|24 - 12| = 12\). Then \(AD + FB=4+12 = 16\) units.

c) \(ED\):

The coordinate of \(E=-8\), \(D = 8\). So \(ED=|8-(-8)|=|8 + 8|=16\) units.

d) \(EF - AF\):

The coordinate of \(E=-8\), \(F = 12\), \(A = 4\). \(EF=|12-(-8)|=20\), \(AF=|12 - 4| = 8\). Then \(EF - AF=20 - 8=12\) units.

e) \(CA\):

The coordinate of \(C=-16\), \(A = 4\). So \(CA=|4-(-16)|=|4 + 16| = 20\) units.

f) \(AB\):

The coordinate of \(A = 4\), \(B = 24\). So \(AB=|24 - 4|=20\) units.

For 2:

a) \(PS+RQ\):

The coordinate of \(P = 12\), \(S = 18\), \(R = 36\), \(Q = 72\). \(PS=|18 - 12|=6\), \(RQ=|72 - 36| = 36\). Then \(PS + RQ=6+36 = 42\) units.

b) \(SQ\):

The coordinate of \(S = 18\), \(Q = 72\). So \(SQ=|72 - 18|=54\) units.

c) \(PQ - RT\):

The coordinate of \(P = 12\), \(Q = 72\), \(R = 36\), \(T = 48\). \(PQ=|72 - 12|=60\), \(RT=|48 - 36| = 12\). Then \(PQ - RT=60 - 12=48\) units.

d) \(ST\):

The coordinate of \(S = 18\), \(T = 48\). So \(ST=|48 - 18|=30\) units.

e) \(RT\):

The coordinate of \(R = 36\), \(T = 48\). So \(RT=|48 - 36|=12\) units.

For 3:

a) \(JN\):

The coordinate of \(J=-33\), \(N=-12\). So \(JN=|-12-(-33)|=|-12 + 33| = 21\) units.

b) \(LM+NK\):

The coordinate of \(L=-24\), \(M=-15\), \(N=-12\), \(K = 3\). \(LM=|-15-(-24)|=9\), \(NK=|3-(-12)| = 15\). Then \(LM + NK=9+15 = 24\) units.

c) \(LK\):

The coordinate of \(L=-24\), \(K = 3\). So \(LK=|3-(-24)|=|3 + 24|=27\) units.

d) \(JN - LM\):

We know \(JN = 21\) and \(LM = 9\). Then \(JN - LM=21 - 9=12\) units.

Answer:

1.
a) 40 units
b) 16 units
c) 16 units
d) 12 units
e) 20 units
f) 20 units
2.
a) 42 units
b) 54 units
c) 48 units
d) 30 units
e) 12 units
3.
a) 21 units
b) 24 units
c) 27 units
d) 12 units