Kuala Lumpur Trial 2025 Add Maths Paper 2, Question 9Coordinate Geometry

Solved on video in English · Form 4, Coordinate Geometry · 6:34 video

The question

(a)(i)

Diagram 6 shows the straight line MN and the straight line PQ intersecting at the point Q. The line MN crosses the x-axis at −8 and the y-axis at 4, and P is the point (−6, 11).

(a) Given that the equation of the straight line MN is x/a + y/b = 1, find: (i) the value of a and of b.

(a)(ii)

Diagram 6 shows the straight line MN and the straight line PQ intersecting at right angles at the point Q. The line MN crosses the x-axis at −8 and the y-axis at 4, and P is the point (−6, 11).

(a)(ii) Find the equation of the straight line PQ.

(b)

Diagram 6 shows the straight line MN and the straight line PQ intersecting at Q, with MN crossing the axes at −8 and 4, and P(−6, 11).

(b) The straight line PQ is extended to R such that PQ : PR = 3 : 5. Find the coordinates of point R.

(c)

Diagram 6 shows the straight lines MN and PQ, with R the point found in part (b). [Reconstructed from the marking scheme — see issue] (c) A point moves such that its distance from R is always 4 units. Find the equation of the locus of the point.

Kuala Lumpur Trial 2025 Add Maths Paper 2, Question 9: the question as drawn in Eduly's video6:34

Part (a)(i)

Step 1

In the intercept form x/a + y/b = 1, a is the x-intercept and b is the y-intercept.

Why this step

a sits under x, so it is where the line crosses the x-axis; b sits under y. Swapping them is the classic slip.

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

Final answer

a = −8, b = 4

Where students lose marks

Watch out: a is the x-intercept and b is the y-intercept, so don't swap them, and remember the x-intercept here is −8, not +8.

Part (a)(ii)

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

Final answer

y = −2x − 1

Where students lose marks

Watch out: PQ is perpendicular to MN, so use gradient −2, not ½. Then take care with the sign when expanding −2(x + 6).

Part (b)

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

Final answer

R(2/3, −7/3)

Where students lose marks

Watch out: PQ:PR = 3:5 means PQ:QR = 3:2. Use 3:2 in the section formula, and keep R on the far side of Q.

Part (c)

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

Final answer

9x² + 9y² − 12x + 42y − 91 = 0

Where students lose marks

Watch out: R has y = −7/3, so y − (−7/3) becomes y + 7/3. Also square the 4 to get 16.

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