SPM 2017 Add Maths Paper 2, Question 5Coordinate Geometry

Solved on video in English and Bahasa Melayu · 7 marks · Form 4, Coordinate Geometry · 5:34 video

The question

Solution by scale drawing is not accepted. Diagram 3 shows the locations of town A and town B drawn on a Cartesian plane, with town A at (-4, -1) and town B at (2, 1). PQ is a straight road such that the distance from town A and town B to any point on the road is always equal. (a) Find the equation of PQ. (b) Another straight road, ST with an equation y = 2x + 7 is to be built. (i) A traffic light is to be installed at the crossroads of the two roads. Find the coordinates of the traffic light. (ii) Which of the two roads passes through town C(-4/3, 1)?

[7 marks]

SPM 2017 Add Maths Paper 2, Question 5: the question as drawn in Eduly's video5:34

Step 1

Let T(x, y) be any point on PQ; since the distance from A and B to T is always equal, TA = TB (PQ is the perpendicular bisector of AB)

Why this step

Every point on PQ is equally far from A and B, so TA = TB. This turns 'equal distance' into an equation in x and y.

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

Final answer

(a) 3x + y + 3 = 0; (b)(i) (−2, 3); (b)(ii) Road PQ passes through C, ST does not

Where students lose marks

Watch out: check signs when expanding (x + 4)² and (y − 1)², and test town C in BOTH road equations, not just one.

Watch every step of this question solved on video (5:34), with the reason behind each step and a box that checks your own answer.

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