Selangor Trial 2025 Add Maths Paper 2, Question 9Coordinate Geometry

Solved on video in English · Form 4, Coordinate Geometry · 6:42 video

The question

(a)

Diagram 4 shows line L₁ parallel to line L₂ (the lines make angles θ₁ and θ₂ with the positive x-axis). (a) Show that m₁ = m₂, where m₁ and m₂ are the gradients of lines L₁ and L₂ respectively.

(b)(i)

(b) The quadrilateral PQRS has an area of 36 units². It is given that P(−2, 6), Q(−5, h), R(2, 0), S(k, 7) and h = 3k. (i) Find the values of k.

(b)(ii)(a)

(b)(ii) A point T(x, y) moves along the circumference of the circle with diameter PR. (a) Find the equation of the locus T.

(b)(ii)(b)

(b)(ii)(b) Determine whether the point (−3, 2) lies on the circumference of the circle.

Selangor Trial 2025 Add Maths Paper 2, Question 9: the question as drawn in Eduly's video6:42

Part (a)

Step 1

Because L₁ is parallel to L₂ and the x-axis is a transversal, the angles they make with the x-axis are corresponding angles, so θ₁ = θ₂.

Why this step

Don't just claim θ₁ = θ₂. Give the reason: the x-axis cuts two parallel lines, so θ₁ and θ₂ are corresponding angles.

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

Final answer

Shown

Where students lose marks

Watch out: give the reason θ₁ = θ₂ (corresponding angles), and link gradient to tan θ before writing m₁ = m₂.

Part (b)(i)

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

Final answer

k = −7/3 or k = 65/3

Where students lose marks

Watch out: keep the modulus (±72) so you find both values of k, and substitute h = 3k.

Part (b)(ii)(a)

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

Final answer

x² + y² − 6y − 4 = 0

Where students lose marks

Watch out: PR is the diameter, so the radius is half of PR (√13, not √52).

Part (b)(ii)(b)

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

Final answer

No: −3 ≠ 0, so (−3, 2) is not on the circle

Where students lose marks

Watch out: substitute carefully, and only say "on the circle" if the result is exactly 0.

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