SPM 2023 Add Maths Paper 2, Question 10Coordinate Geometry

Solved on video in English and Bahasa Melayu · Form 4, Coordinate Geometry · 7:14 video

The question

(a)(i)

(Solutions by scale drawing and by vectors are not accepted.) Diagram 5 shows four points A(−1, 0), B(2, 6), C(h, 2) and D on a Cartesian plane. It is given that points B, C and D are collinear such that BC : CD = 1 : 3.

(a)(i) Find the coordinates of D in terms of h.

(a)(ii)

Points A(−1, 0), B(2, 6), C(h, 2), D(4h − 6, −10) with B, C, D collinear (BC : CD = 1 : 3).

(a)(ii) Hence, calculate the value of h if the area of triangle ACD is 27 unit².

(b)(i)

With h = 3, B = (2, 6) and D = (6, −10).

(b)(i) P(x, y) moves such that its distance from point B and point D are equal. Using the distance formula, find the equation of the locus of P.

(b)(ii)

The locus of P is x − 4y − 12 = 0; A(−1, 0), B(2, 6), C(3, 2).

(b)(ii) The locus P intersects the y-axis at point E. Determine whether the straight lines BA and CE are parallel or not.

SPM 2023 Add Maths Paper 2, Question 10: the question as drawn in Eduly's video7:14

Part (a)(i)

Step 1

C divides BD with BC : CD = 1 : 3, so by the section formula C = ((3·xB + 1·xD)/(1 + 3), (3·yB + 1·yD)/(1 + 3)).

Why this step

C is the dividing point between B and D. The nearer point gets the bigger multiplier: B gets 3, D gets 1. Flipping them is the common slip.

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

Final answer

D = (4h − 6, −10)

Where students lose marks

Watch out: C divides BD in 1 : 3, so B is multiplied by 3 and D by 1. Don't flip the ratio.

Part (a)(ii)

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

Final answer

h = 3

Where students lose marks

Watch out: |h| = 3 gives h = 3 or −3. Use the diagram (C in the first quadrant) to reject −3, and check your signs when expanding.

Part (b)(i)

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

Final answer

x − 4y − 12 = 0

Where students lose marks

Watch out: (y + 10)² = y² + 20y + 100, so don't drop the middle term, and divide by 8 to simplify fully.

Part (b)(ii)

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

Final answer

Not parallel (m(BA) = 2, m(CE) = 5/3)

Where students lose marks

Watch out: a wrong locus gives a wrong E. Find E first (x = 0), then compare the two gradients.

Watch every step of this question solved on video (7:14), with the reason behind each step and a box that checks your own answer.

Start 7 days freeAlready a member? Watch it now

No card. Every past-year question on video, in English and BM.

All questions in SPM 2023 Paper 2

Coordinate Geometry: lessons and every past-year question

Baca dalam Bahasa Melayu

More Coordinate Geometry questions

Questions are re-typeset by Eduly for study and commentary. Eduly is not affiliated with Lembaga Peperiksaan Malaysia or the Ministry of Education.