Question

Let ‘O’ and ‘P’ represent the numbers 0 and 3 respectively on the number

line. Points Q, R and S are between ‘O’ and ‘P’ such that OQ = QR = RS = SP.

What are the rational numbers represented by the points Q, R and S?
plz answer I really need it plzzzzzzzzzzzzzz

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Answer 1

Given:

Two points 'O' and 'P' representing the numbers 0 and 3 on the number line.

Points Q, R and S are between ‘O’ and ‘P’ such that OQ = QR = RS = SP

To find:

The rational number represented by points Q, R and S ?

Solution:

First of all, please refer to the attached image for a better understanding of the given situation.

Length OP = 3 units

Let the length of OQ = QR = RS = SP = x units

Now, we can see that:

OQ + QR + RS + SP = OP

Putting the values,

$x+x+x+x=3\\\Rightarrow 4x = 3\\\Rightarrow x = \dfrac{3}{4}$

Q will represent = Position of O + $\frac{3}{4}$

Q = 0 + $\frac{3}{4}$ = $\frac{3}{4}$

R will represent = Position of Q + $\frac{3}{4}$

R = $\frac{3}{4}$ + $\frac{3}{4}$ = $\frac{6}{4}\ or\ \frac{3}2$

S will represent = Position of R + $\frac{3}{4}$

S = $\frac{6}{4}$ + $\frac{3}{4}$ = $\frac{9}{4}$

So, Q, R ans S represent the fractional numbers $\frac{3}{4}, \frac{6}{4}, \frac{9}{4}$ respectively on the number line.