Q22 of 52 Page 1

Find the coordinates of a point P, which lies on the line segment joining the points A(–2, –2) and B(2, 4) such that AP = 3/7 AB.


Given,


AP = 3/7 AB


So,


AP/AB = 3/7


Let AP = 3k


AB = 7k


BP = AB – AP = 7k – 3k = 4k


∴ AP/AB = 3k/7k = 3/4


By section formula, we get;



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20

An ice-cream seller sells his ice creams in two ways:

(A) In a cone of r = 5 cm, h = 8 cm


(B) In a cup in shape of cylinder with r = 5 cm, h = 8 cm


He charges the same price for both but prefers to sell his ice-cream in a cone.


(a) Find the volume of the cone and the cup.


(b) Which out of the two has more capacity?


(c) By choosing a cone, which value is not being followed by the ice-cream seller?


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The angles of depression of the top and bottom of a tower as seen from the top of a 60√3 m high cliff are 45° and 60° respectively. Find the height of the tower.

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Find the area of the quadrilateral ABCD whose vertices are A(–3, 1), B(–2, –4), C(4, –1) and D(3, 4).

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If the points A(x, y), B(3, 6) and C(–3, 4) are collinear, show that x – 3y + 15 = 0.