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Plotting points · 2 marks

Copy the figure and mark S and Q in your diagram. Mark any point P in Quadrant I and any point R in Quadrant III, and write down their coordinates.

xy−8−6−4−2246−4−224OQuadrant IIQuadrant IQuadrant IIIQuadrant IVQ (−5, 3)S (3, −5)
Answer: S (3, −5): 3 right, 5 down. Q (−5, 3): 5 left, 3 up. Any point with both coordinates positive is in Quadrant I, e.g. P (4, 2); any point with both negative is in Quadrant III, e.g. R (−3, −4). (Answers for P and R will vary.)

Step-by-step solution

Given: S (3, −5) is in Quadrant IV; Q (−5, 3) is in Quadrant II

Idea: To plot (x, y), start at O, move x units along the x-axis (right if positive, left if negative), then y units parallel to the y-axis (up if positive, down if negative).

xy−8−6−4−2246−4−224OQuadrant IIQuadrant IQuadrant IIIQuadrant IVQ (−5, 3)S (3, −5)P (4, 2)R (−3, −4)
  1. S (3, −5): from O move 3 units right, then 5 units down. Mark S; it lies in Quadrant IV.½ mark
  2. Q (−5, 3): from O move 5 units left, then 3 units up. Mark Q; it lies in Quadrant II.½ mark
  3. P in Quadrant I: both coordinates must be positive. Choose P (4, 2): 4 right, 2 up.½ mark
  4. R in Quadrant III: both coordinates must be negative. Choose R (−3, −4): 3 left, 4 down.½ mark
  5. Any other choice is correct as long as P has both coordinates positive and R has both coordinates negative (for example P (1.5, 6), R (−7, −2)).
S (3, −5) and Q (−5, 3) are marked as shown. One correct choice is P (4, 2) in Quadrant I and R (−3, −4) in Quadrant III; any P with both coordinates positive and any R with both coordinates negative is correct.

Check: Signs: P (4, 2) is (+, +), Quadrant I ✓; R (−3, −4) is (−, −), Quadrant III ✓.

Answer to write in the exam

S (3, −5): 3 units right, 5 units down → Quadrant IV

Q (−5, 3): 5 units left, 3 units up → Quadrant II

P in Quadrant I (both coordinates positive): P (4, 2)

R in Quadrant III (both coordinates negative): R (−3, −4)

Common mistakes that cost marks

  • Plotting (3, −5) by going 3 up and 5 left. The first number is always the move along the x-axis.
  • Putting S and Q in the same place because they use the same numbers. (3, −5) and (−5, 3) are different points in different quadrants.
  • Choosing R (−3, 4) for Quadrant III. Only one coordinate is negative there, so that point is in Quadrant II.

How this can come in the exam

MCQ (1 mark)

Which of these points lies in Quadrant III?

  1. (−4, 2)
  2. (3, −1)
  3. (−2, −6)
  4. (0, −5)
Show answer

(C) (−2, −6)
Only (−2, −6) has both coordinates negative. (0, −5) is on the y-axis.

Short answer (2 marks)

Plot K (−3, 0), N (−3, 2) and L (0, 2). Name the figure OKNL, where O is the origin, and find its area.

Show answerOK runs 3 units along the x-axis, KN goes 2 units up, NL 3 units right, LO 2 units down; all angles are right angles. OKNL is a rectangle 3 by 2 (1 mark), area = 3 × 2 = 6 square units (1 mark).

Try one yourself

Write a point in each quadrant whose two coordinates add up to 1. Is this possible in every quadrant?

Show answer

Quadrant I: (0.5, 0.5); Quadrant II: (−2, 3); Quadrant IV: (3, −2). Quadrant III is impossible: there both coordinates are negative, so their sum is negative, never 1.

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