SPM 2022 Add Maths Paper 1, Question 15Coordinate Geometry

Solved on video in English and Bahasa Melayu · Form 4, Coordinate Geometry · 6:45 video

The question

(a)

15 (a) Diagram 11 shows a line segment AC with A(x1, y1), B(x, y) and C(x2, y2), where B lies between A and C. It is given that point B divides the line segment AC in the ratio m : n. Show that y = (n·y1 + m·y2)/(m + n).

(b)

15 (b) It is given that P(x, y) moves such that its distance from R(3/2, −1/2) is 2.5 times its distance from the y-axis. Find the equation of the locus of P.

(c)

15 (c) Diagram 12 shows points P, Q, R and S on a Cartesian plane, with Q(2, 12) and S(8, 9). P lies on the y-axis (below Q) and R is above. It is given that W(x, y) moves such that its distance from point P and point R is always equal (the locus passes through Q and S). If the area of the quadrilateral PQRS is 60 unit², find the y-intercept of the straight line PQ.

SPM 2022 Add Maths Paper 1, Question 15: the question as drawn in Eduly's video6:45

Part (a)

Step 1

Since B divides AC in the ratio m : n, the ratio of the y-differences equals m : n: (y − y1)/(y2 − y) = m/n.

Why this step

Don't just quote the formula: derive it. Points on a straight line split the y-distances in the same ratio m : n as the segment itself.

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

Final answer

Shown

Where students lose marks

Watch out: don't just quote the section formula. Derive it from the ratio of y-differences and show the cross-multiplication.

Part (b)

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

Final answer

21x² − 4y² + 12x − 4y − 10 = 0

Where students lose marks

Watch out: use |x| directly for the distance from the y-axis. Leaving it as an unsimplified expression makes the algebra messy.

Part (c)

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

Final answer

y-intercept of PQ = 3

Where students lose marks

Watch out: when using the shoelace formula, write out every cross-multiplication product. Skipping that working loses marks.

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