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TMUA 2017 · Paper 2 · Question 2 of 20

TMUA 2017 Paper 2 Question 2

Coordinate geometry — Coordinate geometry · area of a rectangle. Try it first; the answer and a full worked solution are below.

TMUA 2017 · Paper 2Coordinate geometryCoordinate geometry · area of a rectangle5 options
PQRS is a rectangle.

The coordinates of P and Q are (0, 6) and (1, 8) respectively.

The perpendicular to PQ at Q meets the x-axis at R.

What is the area of PQRS?

  1. A52
  2. B4√10
  3. C20
  4. D8√10
  5. E40
Show the answer and worked solution
answer · E
  1. A52
  2. B4√10
  3. C20
  4. D8√10
  5. E40
The side PQ has gradient 8−61−0 = 2 and length √12 + 22 = √5. The perpendicular at Q has gradient −12, so its equation is y − 8 = −12(x−1); setting y = 0 gives x = 17, so R = (17, 0). Then QR = √162 + 82 = √320 = 8√5, and the area is √5 × 8√5 = 40.