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# 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.

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**Given:**The points P, Q, R, S, T, U, A and B on the number line are such that, $TR = RS = SU$ and $AP = PQ = QB$.

**To do:**To name the rational numbers represented by P, Q, R, and S.

**Solution:**

**Numbers represented by R and S:**

Points U, S, R, and T are on the left of the origin$(0)$.

We know that distance between points U and T is $1\ unit$. The number line is divided into three equal parts between points U and T.

$TR=RS=SU=\frac{1}{3}$

$R=-1+(-\frac{1}{3})$

$=-\frac{4}{3}$

$S=-1+(-\frac{2}{3})$

$=-1-(\frac{2}{3})$

$=-\frac{5}{3}$

**Numbers represented by P and Q:**

Points A, P, Q, and B are on the sight of the origin $(0)$, and the distance between points A and B is $1\ unit$. The number line is divided into three equal parts:

So, $AP=PQ=QB=\frac{1}{3}$

$P=2+\frac{1}{3}=\frac{7}{3}$

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

Therefore, the number represented by $P$ is $\frac{7}{3}$

The number represented by $Q$ is $\frac{8}{3}$

The number represented by $R$ is $-\frac{4}{3}$

The number represented by $S$ is $-\frac{5}{3}$.

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