A(1, 4), B(3, 2) and C(7, 5) are vertices of a triangle ABC. Find :

(i) the co-ordinates of the centroid of triangle ABC.

(ii) the equation of a line, through the centroid and parallel to AB.

A(7, -1), B(4, 1) and C(-3, 4) are the vertices of a triangle ABC. Find the equation of a line through the vertex B and the point P in AC; such that AP : CP = 2 : 3.

The inclination of a line, which is not passing through origin, is 1. Its intercept with both the axes are :

1. equal

2. having same sign

3. equal in magnitude with opposite signs

4. not equal

The line passing through point (1, 1) and making y-intercept equal to 3 has equation :

1. 2x - y = 3

2. 2x - y + 3 = 0

3. 2x + y = 3

4. 2y + x = 3