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Short Questions (Question 1 & 2)

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Question 1:
The vertices of a triangle are P (6, 1), Q (5, 6) and R (m, -1). Given that the area of the triangle is 31 unit2, find the values of m.

Solution:
Area of  △   P Q R  =  31 1 2   | 6  5    m   1  6 − 1    6 1 | = 31 | ( 6 ) ( 6 ) + ( 5 ) ( − 1 ) + ( m ) ( 1 ) − ( 1 ) ( 5 ) − ( 6 ) ( m ) − ( − 1 ) ( 6 ) | = 62 | 36 − 5 + m − 5 − 6 m + 6 | = 62 | 32 − 5 m | = 62 32 − 5 m = ± 62 − 5 m = 62 − 32  or  − 5 m = − 62 − 32 m = − 6  or  m = 94 5



Question 2:
The points P (3m, m), Q (t, u) and R (3t, 2u) lie on a straight line. Q divides PR in the ratio 3 : 2. Express t in terms of u.

Solution:
( ( 3 m ) ( 2 ) + ( 3 t ) ( 3 ) 3 + 2 , ( m ) ( 2 ) + ( 2 u ) ( 3 ) 3 + 2 ) = ( t , u ) 6 m + 9 t 5 = t 6 m + 9 t = 5 t 6 m = − 4 t m = − 2 3 t → ( 1 ) 2 m + 6 u 5 = u 2 m + 6 u = 5 u 2 m = − u From (1), 2 ( − 2 t 3 ) = − u t = 3 4 u