Melaka Trial 2025 Add Maths Paper 1, Question 6Coordinate Geometry

Solved on video in English · Form 4, Coordinate Geometry · 5:00 video

The question

(a)

Diagram 2 shows a straight line AB which intersects the straight line CD at point C. Given that point C divides the line segment AB in the ratio 1:2.

(a) Find the equation of the locus of a point that moves such that its distance from point D is constantly 4 units.

(b)

From the diagram, A = (0, 6) and B = (9, 0).

(b) Hence, determine whether the locus passes through point C. Justify your answer.

Step 1

Let the moving point be P(x, y). Its distance from D(5, 7) is always 4: √((x − 5)² + (y − 7)²) = 4.

Why this step

A locus is every point that obeys one rule. Here the rule is 'distance to D equals 4', so we write that rule using the distance formula.

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

Final answer

x² + y² − 10x − 14y + 58 = 0

Where students lose marks

Watch out: the right-hand side is 4² = 16, not 4. Then check 25 + 49 − 16 = 58 carefully.

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

Final answer

C(3, 4); −3 ≠ 0, so the locus does not pass through C

Where students lose marks

Watch out: use the ratio the right way round in the section formula, and only say 'yes' if the substituted value is 0.

Watch every step of this question solved on video (5:00), with the reason behind each step and a box that checks your own answer.

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