To mark $5$ on the number line by construction, which right triangle should you draw?

Class 9Number SystemsNumber Systems

Step-by-Step Solution

By Pythagoras the hypotenuse is

2^{2} + 1^{2} = 5

; swinging that length onto the line from 0 marks

5

. The other triangles give hypotenuses 2,

26

and

13

Answer: B) Legs 2 and 1

Every real number has a unique location on the number line.

- Rationals: easy to plot.

\frac{3}{4}

→ 3 quarters past 0.
- Irrationals like

2

can be plotted geometrically: a right triangle with legs 1 and 1 has hypotenuse

2

(Pythagoras). Use a compass to mark off

2

on the number line from 0.

You can extend this —

3

from a triangle with legs

2

and 1,

4 = 2, 5

from legs 2 and 1, etc. (the spiral of Theodorus).

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