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Glide Reflections Worksheet

Glide Reflections Worksheet
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1.
What is the measure of the angle between the mirrors for this kaliedoscope image?

 a. 30° b. 45° c. 60° d. 72°

Solution:

The vibrant images of a kaleidoscope are produced by repeated reflections in intersecting mirrors.

The figure is repeated 6 times in 360°.

The measure of the angle between the mirrors = 360 / 6 = 60

Hence the measure of the angle between the mirrors is 60°.

2.
Identify the isometry that maps the image with the original figure.

 a. reflection b. rotation c. glide reflection d. translation

Solution:

An isometry is a transformation in which the original figure and its image are congruent.

The isometry that maps image with the original figure is reflection.

The original figure and its reflection will be on either sides of the line of reflection and will be like mirror images.

3.
Find the image of the polygon ABCD under the glide reflection where the glide is given by the reflection at $x$ = 0 and translated by a vector <- 1, - 5>.

 a. Polygon IJKL b. Polygon MNOP c. Polygon QRST d. Polygon EFGH

Solution:

A glide reflection is the symmetry operation that combines a reflection and a translation.

Identify the points of the vertex A.

The coordinates of A are (1,3).

After reflection at x = 0, The coordinates of A are (- 1, 3).

The value of the x-coordinate is decreased by 1 unit and the value of the y-coordinate is decreased by 5 units.

The coordinates of the vertex A after reflection and then translation = (- 1 - 1, 3 - 5) = ( - 2, - 2)

The polygon with the coordinates of vertex A as ( - 2, - 2) is identified as QRST.

4.
What is the isometry that maps Figure 1 to Figure 3?

 a. glide reflection b. rotation c. reflection d. translation

Solution:

A rotation is the composition of two reflections in intersecting lines.

L1 and L2 are two intersecting lines.

Figure 2 is the reflected image of Figure 1 in line L1.

Figure 3 is the reflected image of Figure 2 in line L2.

Figure 1 is reflected twice over two intersecting lines to get Figure 3.

So, the isometry that maps Figure 1 to Figure 3 is rotation.

5.
Identify the incorrect statement/statements.
I. If more than one transformation is applied it is referred as composition.
II. The transformations rotation and reflection are the only isometries.
III. A composition of two transformations is a transformation in which the second transformation is independent of the image of the first.
IV. Rotation, translation and reflection are transformations that change the position of an object but not its shape or size.
 a. II and III b. IV c. I d. I and II

Solution:

An isometry is a transformation in which the original figure and its image are congruent.

There are four types of isometries. They are rotation, reflection, translation and glide reflection.

A composition of two transformations is a transformation in which the second transformation is performed on the image of the first.

So, the statements II and III are incorrect.

6.
What is the isometry that maps Figure A to Figure B?

 a. translation b. reflection c. rotation d. glide reflection

Solution:

An isometry is a transformation in which the original figure and its image are congruent.

A translation is a transformation that moves figure the same distance as in the same direction.

The figure is moved 5 units right and 4 units up. The translation vector is <5, 4>.

7.
Recognise the design created by glide reflection.

 a. Figure 3 b. Figure 4 c. Figure 2 d. Figure 1

Solution:

A glide reflection is the composition of a translation and a reflection, so it is the composition of 3 reflections.

Figure1 is formed by rotation of 90° at the point shown as the center. In this pattern there are neither reflections nor glide-reflections.

Figure 2 contains glide-reflections. The direction of the glide reflection is parallel to one axis of translation and perpendicular to the other axis of translation. There are neither rotations nor regular reflections.

Figure 3 is a repeating pattern formed by translation, you can slide it along a certain direction a certain distance along the two arrows.

Figure 4 contains 180° rotations, There are translations in this pattern, but no reflections or glide-reflections.

Figure 2 is the design created by glide reflection.

8.
Identify the incorrect statement.
I. A composition of three reflections in lines that intersect in more than one point is called glide reflection.
II. A glide reflection is a symmetry operation that combines reflection and translation.
III. A glide reflection is a combination of two transformations, a reflection over a line followed by a translation in the same direction as the line.
IV. None of these.
 a. II b. III c. I d. IV

Solution:

A composition of three reflections in lines that intersect in more than one point is called glide reflection.

A glide reflection is a symmetry operation that combines reflection and translation.

A glide reflection is a combination of two transformations, a reflection over a line followed by a translation in the same direction as the line.

All the three statements are definition of glide reflection. So, they are correct.

Hence, none of these is the answer.

9.
The pair of figures is congruent. What isometry maps one to other?

 a. glide reflection b. rotation c. translation d. reflection

Solution:

An isometry is a transformation in which the original figure and its image are congruent.

A rotation is the composition of two reflections in intersecting lines.

The figure is reflected twice in intersecting lines L1 and L2.

So, the isometry that maps one figure to the other is rotation.

10.
A row of foot prints is an example of which isometry?
 a. reflection b. rotation c. glide reflection d. translation

Solution:

Each left foot print is the reflection of a right foot print, but it has been translated.

A glide reflection is the composition of a reflection and a translation.

Hence a row of foot prints is an example of glide reflection.