Describing Transformations

———————————————————————————————————————————————————

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.

———————————————————————————————————————————————————

:

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.

———————————————————————————————————————————————————

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.

———————————————————————————————————————————————————

Describe fully the transformations in the applet above.

(1). Transform (i)

(2). Transform (II)

(3). Transform (III)

(4). Transform (iv)

———————————————————————————————————————————————————

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?

———————————————————————————————————————————————————

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