SPM 2018 Add Maths Paper 2, Question 3Coordinate Geometry

Solved on video in English and Bahasa Melayu · 6 marks · Form 4, Coordinate Geometry · 6:02 video

The question

Solution by scale drawing is not accepted. Diagram 1 shows a triangle OAB. (a) Given the area of triangle OAB is 30 unit², find the value of k. (b) Point Q(2, 4) lies on the straight line AB. (i) Find AQ : QB. (ii) Point P moves such that PB = 2PQ. Find the equation of the locus P.

[6 marks]

SPM 2018 Add Maths Paper 2, Question 3: the question as drawn in Eduly's video6:02

Step 1

Use the area formula for O(0,0), A(-6,8), B(k,2): Area = (1/2)|x_O(y_A - y_B) + x_A(y_B - y_O) + x_B(y_O - y_A)| = (1/2)|0(8 - 2) + (-6)(2 - 0) + k(0 - 8)| = (1/2)|-12 - 8k|.

7 more steps, each with the reason for it, in the full solution

Final answer

(a) k = 6; (b)(i) AQ : QB = 2 : 1; (b)(ii) 3x² + 3y² − 4x − 28y + 40 = 0

Where students lose marks

Watch out: reject k = −9 (B is right of the y-axis), and square the 2 in PB = 2PQ to get 4PQ².

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