MRSM Trial 2025 Add Maths Paper 2, Question 8Coordinate Geometry

Solved on video in English · Form 4, Coordinate Geometry · 7:08 video

The question

(a)

Solution by scale drawing is not accepted. Diagram 6 shows triangle RST with R(a, b), S(−2, 0) and T(c, d); point U lies on the straight line RT.

(a) Point U divides the line segment RT in the ratio m : n. Derive the formula for the x-coordinate of the point dividing the line segment.

(b)(i)

Diagram 6 shows triangle RST with R(a, b), S(−2, 0) and T(c, d); point U lies on RT.

(b) It is given that U(6, 2) and 2 RU = UT. (b)(i) Find the coordinates of R and the coordinates of T if b = a + 1 and c = −6d.

(b)(ii)

Triangle RST has R(3, 4), S(−2, 0) and T(12, −2).

(b)(ii) Hence, calculate the area, in unit², of triangle RST.

(c)

Triangle RST has R(3, 4) and S(−2, 0).

(c) Find the equation of the locus of the moving point Q such that triangle RSQ always has a right angle at Q. Is the locus passing through the point (−2, 4)? Give your justification.

MRSM Trial 2025 Add Maths Paper 2, Question 8: the question as drawn in Eduly's video7:08

Part (a)

Step 1

Let the dividing point have x-coordinate x. Since U divides RT with RU : UT = m : n, the horizontal parts are in the same ratio: (x − a)/(c − x) = m/n.

Why this step

Along a straight line, the horizontal gaps split in the same ratio as the lengths, so we can work with x alone.

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

Final answer

x = (mc + na)/(m + n)

Where students lose marks

Watch out: m goes with c and n goes with a. Swapping m and n gives the wrong section formula.

Part (b)(i)

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

Final answer

R(3, 4) and T(12, −2)

Where students lose marks

Watch out: 2 RU = UT means RU : UT = 1 : 2, not 2 : 1. Double-check your simultaneous equations for slips.

Part (b)(ii)

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

Final answer

33 unit²

Where students lose marks

Watch out: careful with negative signs when expanding the shoelace formula, and don't forget the ½ at the front.

Part (c)

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

Final answer

x² + y² − x − 4y − 6 = 0; yes, it passes through (−2, 4) since 0 = 0

Where students lose marks

Watch out: perpendicular means m(QR) × m(QS) = −1, not equal gradients. Mind the sign when expanding, and end with a substitution conclusion.

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