
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.



