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+$\frac{2}{3}$=$\frac{6}{3}$+$\frac{2}{3}$=$\frac{8}{3}$