Prove that the points (1, –2), (3, 0), (1, 2) and (–1, 0) are the vertices of a square.

Find the distance between the following points:

(i) (–6, 7) and (–1, –5)

(ii) (–1, –1) and (8, –2)

(iii) (at₁², 2at₁) and (at₂², 2at₂)

Prove that the points (2, –2), (–2, 1) and (5, 2) are the vertices of a right angled triangle.

Prove that the points (1, 1) (–2, 7) and (3, –3) are collinear.