A(-4, 2), B(0, 2) and C(-2, -4) are vertices of a triangle ABC. P, Q and R are mid-points of sides BC, CA and AB, respectively. Show that the centroid of △PQR is the same as the centroid of △ABC.

Given points A(1, 5), B(-3, 7) and C(15, 9).

(i) Find the equation of a line passing through the mid-point of AC and the point B.

(ii) Find the equation of the line through C and parallel to AB.

(iii) The lines obtained in part (i) and (ii) above, intersect each other at a point P. Find the coordinates of the point P.

(iv) Assign, giving reason, a special name of the figure PABC.

Find the equation of a line passing through the points (7, -3) and (2, -2). If this line meets x-axis at point P and y-axis at point Q; find the co-ordinates of points P and Q.

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

(i) the equation of median BD,

(ii) the equation of altitude AE.