Let us find a point on x-axis which is equidistant from the two points (3, 5) and (1, 3).

Let us show by calculation that the points (2, 1), (0, 0), (–1, 2) and (1, 3) are the angular points of a square.

Let us calculate and see that for what value of y, the distance of the two points (2, y) and (10, –9) will be 10.

Let us write by calculation whether the three points O (0, 0), A(4, 3) and B(8, 6) are collinear.

Let us show that the three points (2, 2), (–2, –2) and are the vertices of an equilateral triangle.