Complete the figure below to form a symmetric figure. WX is the line of symmetry.

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Worked solution

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1. Identify the vertices of the given figure below the line of symmetry.

The vertices of the given figure are at (1,0)(1, 0), (3,−2)(3, -2), (2,−3)(2, -3), (5,−2)(5, -2), (8,−3)(8, -3), and (5,0)(5, 0).

2. Reflect each vertex across the line of symmetry WX ($y = 0$).

For a reflection across the horizontal line y=0y = 0, the xx-coordinate remains the same and the yy-coordinate changes sign.

  • (1,0)→(1,0)(1, 0) \rightarrow (1, 0)
  • (3,−2)→(3,2)(3, -2) \rightarrow (3, 2)
  • (2,−3)→(2,3)(2, -3) \rightarrow (2, 3)
  • (5,−2)→(5,2)(5, -2) \rightarrow (5, 2)
  • (8,−3)→(8,3)(8, -3) \rightarrow (8, 3)
  • (5,0)→(5,0)(5, 0) \rightarrow (5, 0)

3. Connect the reflected vertices to complete the figure.

Draw straight line segments connecting the reflected points in the same sequence:

  • From (1,0)(1, 0) to (3,2)(3, 2)
  • From (3,2)(3, 2) to (2,3)(2, 3)
  • From (2,3)(2, 3) to (5,2)(5, 2)
  • From (5,2)(5, 2) to (8,3)(8, 3)
  • From (8,3)(8, 3) to (5,0)(5, 0)
Answer

Draw straight line segments connecting the points (1,0)(1, 0) to (3,2)(3, 2), (3,2)(3, 2) to (2,3)(2, 3), (2,3)(2, 3) to (5,2)(5, 2), (5,2)(5, 2) to (8,3)(8, 3), and (8,3)(8, 3) to (5,0)(5, 0) on the grid.

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