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The coordinates of the figure ABCD are ​A(3​,4​), ​B(6​,4​), ​C(6​,8​), and ​D(3​,8​). The coordinates of the figure HIJK are ​H(negative 1​,0​), ​I(negative 1​,negative 3​), ​J(negative 5​,negative 3​), and ​K(negative 5​,0​). Describe the sequence of rigid motions. Use pencil and paper. Describe a different sequence of rigid motions that will still map ABCD to HIJK.

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sqdancefan

Answer:

  1. reflection across the line x+y=3
  2. reflection across the y-axis, then rotation CCW 90° about (0, 3)

Step-by-step explanation:

The points ABCD are in a CCW sequence; the points HIJK are in a CW sequence. This means at least one reflection is involved in transforming one figure to the other.

1. The perpendicular bisectors of AH and DK are the same line: x+y=3. This means that the figure can be transformed from ABCD to HIJK by reflection across the line x+y=3.

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2. Reflection across a line with a slope of -1 is equivalent to a combination of reflection and rotation. An alternate transformation could be ...

  • reflection across the y-axis
  • rotation about the point (0, 3)

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Further comment

Since the line of reflection is not through the origin, and the center of rotation is not the origin, one could do reflections and rotations with a different line or center, followed by translation to move the figure to the right end position.

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