Question

LAt O, P and Z represent the numbers 0, 3 and -5 respectively on the number line.
Points Q, R and S are between 0 and P such that OQ = QR = RS = SP.
What are the rational numbers represented by the points Q, R and S?
Next choose a point T between Z and 0 so that ZT = TO.
Which rational number does T represent?

5/3 is answer how it is answer​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

CONCEPT

On the real line R the origin is denoted by O and it represents the point 0

Now the point on the left side of the origin is negative and the point on the right side of the origin is positive

GIVEN

O, P and Z represent the numbers 0, 3 and -5 respectively on the number line. Points Q, R and S are between 0 and P such that OQ = QR = RS = SP

Point T between Z and 0 so that ZT = TO

TO DETERMINE

1. The rational numbers represented by the points Q, R and S

2. The rational number represented by T

EVALUATION

A real line is drawn by the given conditions ( Refer to the attachment)

QUESTION : 1

Here OQ = QR = RS = SP

So the distance between O & P are divided into Four parts

So

$\displaystyle \: OQ = \frac{3}{4} \: unit, OR = \frac{6}{4} = \frac{3}{2} \: unit \: , OS \: = \frac{9}{4} \: \: unit$

Since Q, R, S are the points on the right side of the origin

Hence

The rational numbers $\displaystyle \: \frac{3}{4} \:, \frac{3}{2} \: \:, \frac{9}{4} \:$ represented by the points Q, R and S respectively

QUESTION : 2

The distance between O & Z is 5 unit

Now choose a point T between Z and 0 so that ZT = TO

So T is the middle point of ZO

Since T is a point left of the origin

SO T represents the rational number $\displaystyle \: - \frac{5}{2}$