SPM 2021 Add Maths Paper 2, Question 9Coordinate Geometry

Solved on video in English and Bahasa Melayu · Form 4, Coordinate Geometry · 5:36 video

The question

(a)

Solution by scale drawing is not accepted. Diagram 5 shows triangles ABC and CDE. The straight line AE intersects the straight line BD at point C. The coordinates are A(3, 2), B(−1, −8) and E(7, −6). It is given that C is the midpoint of AE and BC : CD = 2 : 3. (a)(i) Find the coordinates of D. (a)(ii) Find the area, in unit², of triangle CDE.

(b)

Using A(3, 2), B(−1, −8) from Diagram 5 and C(5, −2): (b) A point P moves along the circumference of a circle with diameter AB. (b)(i) Find the equation of the locus of P. (b)(ii) Hence, determine whether the locus of P passes through point C.

SPM 2021 Add Maths Paper 2, Question 9: the question as drawn in Eduly's video5:36

Part (a)

Step 1

C is the midpoint of AE: C = ((3 + 7)/2, (2 + (−6))/2) = (5, −2).

Why this step

C lies on both AE and BD. AE gives us C directly, and once we know C, the ratio on BD lets us find D.

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

Final answer

D = (14, 7); area of triangle CDE = 27 unit²

Where students lose marks

Watch out: take care with signs when solving for D, and show every product in the area working, not just 27.

Part (b)

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

Final answer

x² + y² − 2x + 6y − 19 = 0; No, the locus does not pass through C

Where students lose marks

Watch out: the circle's centre is the midpoint of AB, so find it first. Then substitute C carefully into the locus equation.

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