Plotting the Locus of Points with Squared Distance 1 from the Origin

To plot the locus of points whose squared distance from the origin is 1, we need to find all points (x1, x2) such that d(O, P)^2 = 1.

Using the definition of distance from the origin, we have: d(O, P) = max(|x1|, |x2|)

Squaring both sides: d(O, P)^2 = (max(|x1|, |x2|))^2

Since we want the squared distance to be 1, we have: (max(|x1|, |x2|))^2 = 1

Taking the square root of both sides: max(|x1|, |x2|) = 1

This means that either |x1| = 1 and |x2| = 0, or |x1| = 0 and |x2| = 1.

For |x1| = 1 and |x2| = 0, we have two possibilities:

1. x1 = 1 and x2 = 0, which gives us the point (1, 0).
2. x1 = -1 and x2 = 0, which gives us the point (-1, 0).

For |x1| = 0 and |x2| = 1, we also have two possibilities:

1. x1 = 0 and x2 = 1, which gives us the point (0, 1).
2. x1 = 0 and x2 = -1, which gives us the point (0, -1).

Therefore, the locus of points whose squared distance from the origin is 1 is the set of points {(1, 0), (-1, 0), (0, 1), (0, -1)}.

Plotting these points on a graph, we see that they form a square centered at the origin with side length 2.