GLIDE REFLECTIONS AND COMPOSITIONS WORKSHEET

Problem 1 :

Use the information below to sketch the image of ΔABC after a glide reflection.

P(- 1, - 3), Q(- 4, - 1), R(- 6, - 4)

Translation : (x, y) ----> (x + 10, y)

Reflection : in the x-axis

Problem 2 :

Sketch the image of AB after a composition of the given rotation and reflection.

A(2, - 2) and B(3, - 4)

Rotation : 90° counterclockwise about the origin

Reflection : in the y-axis

Problem 3 :

Repeat problem 2, but switch the order of the composition by performing the reflection first and the rotation second. What do you notice?

Problem 4 :

Describe the composition of transformations in the diagram.

Problem 5 :

The mathematical game pentominoes is a tiling game that uses twelve different types of tiles, each composed of five squares. The tiles are referred to by the letters they resemble. The object of the game is to pick up   and arrange the tiles to create a given shape. Use  compositions of transformations to describe how the tiles below will complete the 6 X 5 rectangle.

1. Answer :

Begin by graphing ΔPQR. Then, shift the triangle 10 units to the right to produce ΔP'Q'R'.

Finally, reflect the triangle ΔP'Q'R' in x-axis to produce ΔP"Q"R".

In the above problem, try reversing the order of the transformations. Notice that the resulting image will have the same coordinates as ΔP"Q"R" above. This is true because the line of reflection is parallel to the direction of the translation.

2. Answer :

Begin by graphing AB. Then, rotate the segment 90° counterclockwise about the origin to produce A'B'.

Finally, reflect the segment A'B' in y-axis to produce A"B".

3. Answer :

Begin by graphing AB. Then, reflect the segment in y-axis to produce A'B'.

Finally, rotate the segment A'B' 90° counterclockwise about the origin to produce A"B".

Instead of being in Quadrant II, as given in the example on finding the image of a composition, the image is in Quadrant IV.

The order which the transformations are performed affects the final image.

4. Answer :

Two transformations are shown. First figure PQRS is reflected in the line x = 2 to produce figure P'Q'R'S'. Then figure P'Q'R'S' is rotated 90° clockwise about the point (2, 0) to produce P"Q"R"S".

5. Answer :

Step 1 :

To complete part of the rectangle, rotate the A tile 90° clockwise, reflect the tile over a horizontal line, and translate it into place.

Step 2 :

To complete the rest of the rectangle, rotate the D tile 90° clockwise, reflect the tile over a vertical line, and translate it into place.

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