The line segment joining A(2, -3) and B(-3, 2) is intercepted by the x-axis at the point M and the y-axis at the point N. PQ is perpendicular to AB at R and meets the y-axis at a distance of 6 units form the origin O, as shown in the diagram, at S. Find the :

(a) coordinates of M and N.

(b) coordinates of S

(c) slope of AB.

(d) equation of line PQ.

The angles of depression of two ships A and B on opposite sides of a light house of height 100 m are respectively 42° and 54°. The line joining the two ships passes through the foot of the light house.

(a) Find the distance between the two ships A and B.

(b) Give your final answer correct to the nearest whole number.

(Use mathematical tables for this question)

ABCD is a cyclic quadrilateral in which BC = CD and EF is a tangent at A. ∠CBD = 43° and ∠ADB = 62°. Find :

(a) ∠ADC

(b) ∠ABD

(c) ∠FAD

A(a, b), B(-4, 3) and C(8, -6) are the vertices of a △ ABC. Point D is on BC such that BD : DC is 2 : 1 and M(6, 0) is mid-point of AD. Find :

(a) coordinates of point D.

(b) coordinates of point A.

(c) equation of a line parallel to line BC, through M.