Mathematics

Problem

A student draws a right-angled triangle

\triangle ABC

on paper where

AB = 3\,\text{cm}

and

BC = 4\,\text{cm}

. She places point

A

on the origin

O

of a horizontal number line and swings the hypotenuse

AC

so that it lies on the positive axis with one end at

O

and the other at point

P

. a. (i) Without measuring, determine the exact distance

OP

. b. (ii) Write the value obtained in part (i) correct to three decimal places. c. (iii) Explain how a similar procedure can now be used to locate the point representing

\sqrt{10}

on the same number line.

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