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.

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.

__

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

_____

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.

perimeter : 46

area : 79.75