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Question 13
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If x = and y= , find, correct to 1 decimal place, | x + y|.
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P(6, 4), Q(-2, -2) and R(4, -6) are the vertices of triangle PQR.
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Determine the coordinates of M and S, the midpoints of and respectively.
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Find and .
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State the relationship between and .
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Find the equation of .
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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.
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