The coordinates of the vertices of a triangle are (–1, 5), (3, 7), (3, 1). Find the coordinates of its centroid.

In the picture, the midpoints of the sides of the large quadrilateral are joined to draw the small quadrilateral inside.

i) Find the coordinates of the fourth vertex of the small quadrilateral.

ii) Find the coordinates of the other three vertices of the large quadrilateral.

The vertices of a triangle are the points with coordinates (3, 5), (9, 13), (10, 6). Prove that the triangle is isosceles. Calculate is area.

The centre of circle is (1, 2) and (3, 2) is a point on it. Find the coordinates of the other end of the diameter through this point.

Prove that the points (1, 8), (2, 5), (3, 7) are on the same line.