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  PQR = 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 | 365+m56m+6|=62 | 32 5m|=62 325m=±62 5m=6232 or 5m=6232 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:
( ( 3m )( 2 )+( 3t )( 3 ) 3+2 , ( m )( 2 )+( 2u )( 3 ) 3+2 )=( t,u ) 6m+9t 5 =t 6m+9t=5t 6m=4t m= 2 3 t(1) 2m+6u 5 =u 2m+6u=5u 2m=u From (1), 2( 2t 3 )=u t= 3 4 u