The diagram below is only half a symmetrical figure. Complete the figure.

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Worked solution

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1. Identify the line of symmetry and the reflection rule

The line of symmetry is y=14−xy = 14 - x, which means x+y=14x + y = 14. For any point (x,y)(x, y), its reflection across this line is (14−y,14−x)(14 - y, 14 - x).

2. Reflect each vertex across the line of symmetry

Reflecting the given vertices:

  1. (2,12)→(14−12,14−2)=(2,12)(2, 12) \rightarrow (14-12, 14-2) = (2, 12) (on the line)
  2. (2,9)→(14−9,14−2)=(5,12)(2, 9) \rightarrow (14-9, 14-2) = (5, 12)
  3. (4,9)→(14−9,14−4)=(5,10)(4, 9) \rightarrow (14-9, 14-4) = (5, 10)
  4. (4,8)→(14−8,14−4)=(6,10)(4, 8) \rightarrow (14-8, 14-4) = (6, 10)
  5. (2,6)→(14−6,14−2)=(8,12)(2, 6) \rightarrow (14-6, 14-2) = (8, 12)
  6. (7,4)→(14−4,14−7)=(10,7)(7, 4) \rightarrow (14-4, 14-7) = (10, 7)
  7. (8,2)→(14−2,14−8)=(12,6)(8, 2) \rightarrow (14-2, 14-8) = (12, 6)
  8. (11,3)→(14−3,14−11)=(11,3)(11, 3) \rightarrow (14-3, 14-11) = (11, 3) (on the line)

3. Connect the reflected vertices to complete the figure

Connect the points in order: (11,3)→(12,6)→(10,7)→(8,12)→(6,10)→(5,10)→(5,12)→(2,12)(11, 3) \rightarrow (12, 6) \rightarrow (10, 7) \rightarrow (8, 12) \rightarrow (6, 10) \rightarrow (5, 10) \rightarrow (5, 12) \rightarrow (2, 12).

Answer

The completed figure is drawn by reflecting the given vertices across the line of symmetry y=14−xy = 14 - x. The new vertices are (5,12)(5, 12), (5,10)(5, 10), (6,10)(6, 10), (8,12)(8, 12), (10,7)(10, 7), (12,6)(12, 6), connected in reverse order from (11,3)(11, 3) to (2,12)(2, 12).

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