SPM 2017 Add Maths Paper 1, Question 18Coordinate Geometry

Solved on video in English and Bahasa Melayu · 3 marks · Form 4, Coordinate Geometry · 3:41 video

The question

A straight line passes through P(3, 1) and Q(12, 7). The point R divides the line segment PQ such that 2PQ = 3RQ. Find the coordinates of R.

[3 marks]

Step 1

From 2PQ = 3RQ, PQ/RQ = 3/2. Since R lies between P and Q, PQ = PR + RQ, so (PR+RQ)/RQ = 3/2, giving PR/RQ = 1/2, i.e. PR : RQ = 1 : 2.

Why this step

The formula needs the parts PR : RQ, not the whole PQ : RQ. So replace PQ with PR + RQ. Just reading off 3:2 or 2:3 is the classic mistake.

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

Final answer

R = (6, 3)

Where students lose marks

Watch out: don't use 2:3 or 3:2 straight from 2PQ = 3RQ. Work out PR : RQ = 1 : 2 first, then use the section formula.

Watch every step of this question solved on video (3:41), with the reason behind each step and a box that checks your own answer.

No card. Every past-year question on video, in English and BM.