The points P,Q,R,S,T,U,A and B on the number line are such that, TR=RS=SU and AP=PQ=QB. Name the rational numbers represented by P,Q,R and S.
P=83,Q=73,R=−43,S=−53
P=73,Q=73,R=−53,S=−43
P=73,Q=83,R=−43,S=−53
P=83,Q=73,R=−53,S=−43
A
P=73,Q=73,R=−53,S=−43
B
P=73,Q=83,R=−43,S=−53
C
P=83,Q=73,R=−43,S=−53
D
P=83,Q=73,R=−53,S=−43
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Solution
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from the given number line, we can observe that the points U,T are −1−(−2)=1 unit distance apart.
Given that the points are such that TR=RS=SU.
Therefore, TR=RS=SU=13.
The point S is at −2+13=−53
The point R is at −2+13+13=−43
from the given number line, we can observe that the points $A,B$are3-2=1$ unit distance apart.
Given that the points are such that AP=PQ=QB.
Therefore, AP=PQ=QB=13.
The point P is at 2+13=73
The point Q is at 2+13+13=83
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