| 
          
            
              
                
                  Question 13   
                           
                    | 
                 
                
                
                  
                    - 
                      
If  x =    and  y=   , find, correct to 1  decimal place, | x +  y|.   
                     
                    - 
                      
P(6, 4), Q(-2, -2) and R(4, -6) are the vertices of triangle PQR.  
                     
                    - 
                      
Determine the coordinates of M and S, the  midpoints of    and    respectively.   
                     
                    - 
                      
Find   and   .   
                     
                    - 
                      
State the relationship between   and   .   
                     
                    - 
                      
Find the equation of   .   
                     
                   
                   | 
                 
                
                   | 
                 
                
                  
                    The Chief Examiner reported that this  question was the most unpopular question and majority of those who attempted it  performed poorly. 
In part (a), candidates were expected  respond as follows: 
 x + y =   +   = . Therefore, |x + y| =   = 5  = 7.1. 
In part (b), candidates were expected to  show that if M(x, y) was the midpoint of   , then x =   = 2 and y =   = 1. Hence, the required point was M(2, 1).  Similarly, if S(x, y) was the midpoint of  , then, x =   = 5 and y =   = -1. Therefore, the midpoint of   was S(5, -1).   =   -   =  . Similarly,   =   -  =  . By comparing the two  vectors they would conclude that   = 2 . To find the equation  of , candidates would  first find the gradient of   as   =  . The required equation  was y – 1 = (x – 2) which  simplified to 2x + 3y =  7.  
                     
                     
                    | 
                 
                
                   | 
                 
                | 
             
            |