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.



(4 Marks)

Answer 1

By observing the figure, we can say that,

The distance between A and B = 1 unit

And it is divided into 3 equal parts = AP = PQ = QB = $\frac{1}{3}$

P $=2+\left(\frac{1}{3}\right)=\frac{(6+1)}{3}=\frac{7}{3}$

(1 Mark)

Q $=2+\left(\frac{2}{3}\right)=\frac{(6+2)}{3}=\frac{8}{3}$

(1 Mark)

Similarly,

The distance between U and T = 1 unit

And it is divided into 3 equal parts = TR = RS = SU = $\frac{1}{3}$

R =$-1-\left(\frac{1}{3}\right)=\frac{(-3-1)}{3}=\frac{-4}{3}$

(1 Mark)

S = $-1-\left(\frac{2}{3}\right)=\frac{(-3-2)}{3}=\frac{-5}{3}$

(1 Mark)