A(–1, 3), B(4, 2) and C(3, –2) are the vertices of a triangle.

(i) Find the co-ordinates of the centroid G of the triangle.

(ii) Find the equation of the line through G and parallel to AC.

Find the equation of a line passing through the point P(–2, 1) and parallel to the line joining the points A(4, –3) and B(–1, 5).

Find the equation of a line passing through the origin and parallel to the line 3x – 2y + 4 = 0.

Find the equation of the line that has x-intercept –3 and is perpendicular to the line 3x + 5y = 1.