SPM 2024 Add Maths Paper 2, Question 11Coordinate Geometry

Solved on video in English and Bahasa Melayu · Form 4, Coordinate Geometry · 5:09 video

The question

(a)

Solution by scale drawing and/or vector are not accepted.

Diagram 5 shows the triangle PQR on a Cartesian plane. It is given that the gradient of the straight lines PQ, QR and PR is −3m, m and 3m respectively, such that m is a constant.

(a) Show that m = 1/2.

Show that m = 1/2.

(b)

(b) Find the coordinates of R.

Find the coordinates of R.

(c)(i)

(c)(i) Find the area of △PQR.

Find the area of △PQR.

(c)(ii)

(c)(ii) Point U moves such that its distance from point R is always 5/2 times its distance from point Q.

Find the equation of the locus of U.

Point U moves such that its distance from point R is always 5/2 times its distance from point Q.

Find the equation of the locus of U.

Part (a)

Step 1

Gradient of PQ using coordinates P(1, 1) and Q(−1, 4): m_PQ = (4 − 1)/(−1 − 1) = 3/(−2) = −3/2.

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

Final answer

Shown (m = 1/2)

Where students lose marks

Watch out: from −3m = −3/2, the answer is m = 1/2, not 2. Divide −3/2 by −3: that is 1/2.

Part (b)

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

Final answer

R = (5, 7)

Where students lose marks

Watch out: check the sign in point-gradient form. For PR through P(1, 1) use (x − 1); a wrong sign gives the wrong R.

Part (c)(i)

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

Final answer

12 units²

Where students lose marks

Watch out: use R = (5, 7) from part (b). A wrong R carried forward gives 4 units² instead of 12 units².

Part (c)(ii)

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

Final answer

7x² + 7y² + 30x − 48y + 43 = 0

Where students lose marks

Watch out: setting up UR = (5/2)UQ is not enough. Square 5/2 to 25/4 and simplify slowly; most slips happen in the algebra.

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