P and Q are two points on the x-axis and y-axis respectively. M(3, 2) divides the line segment PQ in the ratio 2 : 3. Find :

(i) the co-ordinates of the points P and Q

(ii) the slope of line segment PQ

(iii) the equation of the line through point P and perpendicular to PQ.

The upper part of a tree is broken over by the wind and makes an angle of 42° with the ground. The horizontal distance from the root of the tree to the point where the top of tree meets the ground is 20 m. Find the height of the tree before it was broken.
Give your answer correct to the nearest whole number.

In the given figure, O is the center of the circle, AB is diameter and CPD is a tangent to the circle at P. If ∠BPD = 30°, find :

(i) ∠APC

(ii) ∠BOP

(iii) ∠OAP

Given a line segment AB joining the points A(-4, 6) and B(8, 3). Find :

(i) the ratio in which line segment AB is divided by y-axis.

(ii) the co-ordinates of the point of intersection.

(iii) equation of perpendicular bisector of AB.