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TMUA 2021 · Paper 1 · Question 9 of 20

TMUA 2021 Paper 1 Question 9

Graphs and transformations — Graphs with modulus · area of the enclosed region. Try it first; the answer and a full worked solution are below.

TMUA 2021 · Paper 1Graphs and transformationsGraphs with modulus · area of the enclosed region7 options
Find the area enclosed by the graph of |x| + |y| = 1
  1. A12
  2. B1
  3. C2
  4. D4
  5. E12√2
  6. F√2
  7. G2√2
Show the answer and worked solution
answer · C
  1. A12
  2. B1
  3. C2
  4. D4
  5. E12√2
  6. F√2
  7. G2√2
Take the four sign cases in turn. In the first quadrant the equation is x + y = 1, a straight segment from (1, 0) to (0, 1); the other three quadrants give the reflections of it. So the graph is a square with vertices (1, 0), (0, 1), (−1, 0), (0, −1), tilted at 45∘. Its diagonals both have length 2, so the area is 12 × 2 × 2 = 2. Reading the 1 as a side length rather than a half-diagonal is the tempting error.