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4024/22 May/Jun 2021, Question 6: The Perpendicular Bisector

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 10 marks

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The question, in short

Find a possible point R so that triangle PQR is isosceles with PR = QR, given P(1, 5) and Q(5, 1), then match three curve sketches to equations and find a perpendicular bisector line.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Using P(1, 5) and Q(5, 1), determine coordinates of one possible R making PR = QR, with angle PRQ not 90 degrees.

  1. 1R is on the perpendicular bisector of PQ, which is the line y = x
  2. 2Avoid (3, 3) (midpoint) and (1, 1), (5, 5) (right angle)
  3. 3e.g. R = (6, 6)

Answer(a, a) with a ≠ 1, 3 or 5

Part (b) · 3 marks

Match each of the three given sketches to the correct equation from the five listed curves.

  1. 1Left: U-shape through O → y = x² − 3x
  2. 2Middle: ∩-shape, maximum on the y-axis → y = 2 − x²
  3. 3Right: cubic with a flat section, crossing at y = −2 → y = x³ − 2

AnswerLeft: y = x² − 3x Middle: y = 2 − x² Right: y = x³ − 2

Part (c) · 5 marks

For A(−1, −5) and B(3, 3), find the equation of the line through the midpoint of AB perpendicular to AB.

  1. 1Gradient AB = (3 − (−5))/(3 − (−1)) = 8/4 = 2
  2. 2Perpendicular gradient = −1/2
  3. 3Midpoint of AB = (1, −1)
  4. 4−1 = −1/2 × 1 + c → c = −1/2
  5. 5y = −(1/2)x − 1/2

Answery = −(1/2)x − 1/2

Stuck on a step? Read the free lesson: The Perpendicular Bisector

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Also searched as: 4024/22/M/J/21 · 4024_s21_qp_22 · 4024 s21 22 · question 6.
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