# Describing Transformations

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Exploring Transformations.

• The tranformation chosen by default in the applet below is Rotation and the center is (1, 1).ā Move the center from the blue point and observe the new positions of the image as it moves in a clockwise direction.
• Pause and alter the angle of rotation and continue to change the center of rotation.
• Choose Reflection on the slider. Note the mirror line and its equation.
• Choose Enlargement. The default scale factor is 2 and the center of enlargement is also (1, 1).
• Alter the scale factor.
• Now, choose Translation on the slider. Note the translation factor.
• use the horizontal or vertical sliders to change the factor.

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Reflecting Polygons on the Coordinate Axes.

Here is Trapezoid A in the coordinate plane.
1. Draw Polygon B, the image of A, using the -axis as the line of reflection.
2. Draw Polygon C, the image of B, using the -axis as the line of reflection.
3. Draw Polygon D, the image of C, using the -axis as the line of reflection.

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Perform Combined Transformations on a Polygons on the Coordinate Axes.

• Draw the image of quadrilateral after a translation that takes B to D.
• Draw the image of quadrilateral after a rotation about point A by angle DAB, counterclockwise.
• Draw the image of quadrilateral after a reflection over segment BC.

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Describe fully the transformations in the applet above.

(1). Transform (i)

(2). Transform (II)

(3). Transform (III)

(4). Transform (iv)

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Andre performs a 90-degree counterclockwise rotation of Polygon P and gets Polygon Pā, but he does not say what the center of the rotation is.

What is the center of rotation?

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Describe a sequence of transformations for which Triangle B is the image of Triangle A.