A line through point P(4, 3) meets x-axis at point A and the y-axis at point B. If BP is double of PA, find the equation of AB.

M is the mid-point of a line segment AB; AXB and MYB are equilateral triangles on opposite sides of AB; XY cuts AB at Z. Prove that : AZ = 2ZB.

The given figure shows a trapezium in which AB is parallel to DC and diagonals AC and BD intersect at point O. If BO : OD = 4 : 7, find :

(i) △AOD : △AOB

(ii) △AOB : △ACB

(iii) △DOC : △AOB

(iv) △ABD : △BOC

A model of a ship is made to a scale of 1 : 160. Find :

(i) the length of the ship, if the length of its model is 1.2 m

(ii) the area of the deck of the ship , if the area of deck of its model is 1.2 m².

(iii) the volume of the ship, if the volume of its model is 1.2 m³.