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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 $-\frac{5}{3}$.
Updated on: 10-Oct-2022
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