Question

(b) Prove that the points (0, 0), (1, 0), (1, 1), and (0, 1) are the vertices of a

unit square. Also plot the square on graph paper.

Answer 1

Proof:

The slope of (0,0) to (1,0) is undefined (the denominator is 0). Same with (1,1) to (0,1).

The slope of (0,0) to (0,1) and (0,1) to (1,1) is 0.

There are two parallel lines, and the slope are negative reciprocals of each other, meaning they're perpendicular.

The distance of the points are all 1.

Therefore, it fits the requirements of a square.