Coordinate Geometry Short Questions (Question 1 & 2)


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 (3mm), (t, u) and (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


Leave a Reply

Your email address will not be published. Required fields are marked *