SPM 2020 Add Maths Paper 1, Question 13Coordinate Geometry

Solved on video in English and Bahasa Melayu · 3 marks · Form 4, Coordinate Geometry · 4:37 video

The question

Diagram 5 shows a triangle ABC on a Cartesian plane with B(4, 5), C(10, 3) and A(p, 2q). It is given the area of the triangle ABC is 20 unit². Express the correct equation of p in terms of q. State a condition for the equation.

[3 marks]

SPM 2020 Add Maths Paper 1, Question 13: the question as drawn in Eduly's video4:37

Step 1

Use the area formula with the shoelace arrangement of A(p, 2q), B(4, 5), C(10, 3): Area = (1/2)|(p5 + 43 + 102q) - (2q4 + 510 + 3p)| = 20.

Why this step

Area is never negative, but the cross-multiplied value can be, depending on corner order. That is why the modulus bars stay, and they matter in the next step.

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

Final answer

p = 39 − 6q or p = −1 − 6q; for the diagram, p = −1 − 6q with q < −1/6

Where students lose marks

Watch out: the modulus gives two cases. Write both p = 39 − 6q and p = −1 − 6q, not just one.

Watch every step of this question solved on video (4:37), with the reason behind each step and a box that checks your own answer.

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