Question

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.

Answer 1

Distance between U and T = 1 unit
It is divided into 3 equal parts.
TR=RS=SU=\(\frac{1}{3}\)
R=-1-\(\frac{1}{3}\)=\(\frac{-3}{3}\)-\(\frac{1}{3}\)=\(\frac{-4}{3}\)
S=\(\frac{-3}{3}\)-\(\frac{2}{3}\)=\(\frac{-5}{3}\)
Similarly,
AB = 1 unit
It is divided into 3 equal parts.
P=2+\(\frac{1}{3}\)=\(\frac{6}{3}\)+\(\frac{1}{3}\)=\(\frac{7}{3}\)
Q=2+\(\frac{2}{3}\)=\(\frac{6}{3}\)+\(\frac{2}{3}\)=\(\frac{8}{3}\)