Position of two points relative to a line — A/L Combined Mathematics

How do I practise Position of two points relative to a line?

1 question with a worked solution

1. What is the relative position of the points P(1, 2) and Q(3, -1) with respect to the straight line L ≡ 2x + 3y - 6 = 0?
   1. A) P and Q lie on opposite sides of the line
   2. B) P lies on the line and Q lies off the line
   3. C) Both P and Q lie exactly on the line
   4. D) P and Q lie on the same side of the line
   Check my answer

   Correct answer: A) P and Q lie on opposite sides of the line

   Evaluating L(x, y) = 2x + 3y - 6 at both points: For P(1, 2): L(1, 2) = 2(1) + 3(2) - 6 = 2 + 6 - 6 = +2 (> 0). For Q(3, -1): L(3, -1) = 2(3) + 3(-1) - 6 = 6 - 3 - 6 = -3 (< 0). Because the evaluated values have opposite algebraic signs (+2 and -3), P and Q lie on opposite sides of the line.

   Show worked solution

   Step 1: Test P(1, 2): 2(1) + 3(2) - 6 = +2 (positive). Step 2: Test Q(3, -1): 2(3) + 3(-1) - 6 = -3 (negative). Step 3: Opposite signs indicate points lie on opposite sides of the line. Answer: P and Q lie on opposite sides of the line.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Position of two points relative to a line fit in the syllabus?

Year 1 · Term 3