The following question is about representing irrational numbers on the number line.
a. (i) Explain, with reasons, why a point obtained by drawing a right-angled triangle whose perpendicular and base are each 1 unit long, and then placing its hypotenuse on the positive real axis with one end at 0, represents the number 2 on the number line.
b. (ii) Describe how this idea can be extended to represent n for any positive integer n on the number line. In your explanation, clearly state the geometric principle you are using in each step.