Glide Reflections Worksheet

**Page 1**

1.

What is the measure of the angle between the mirrors for this kaliedoscope image?

a. | 30° | ||

b. | 45° | ||

c. | 60° | ||

d. | 72° |

The figure is repeated 6 times in 360°.

The measure of the angle between the mirrors =

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

Correct answer : (3)

2.

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

a. | reflection | ||

b. | rotation | ||

c. | glide reflection | ||

d. | translation |

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.

Correct answer : (1)

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 |

Identify the points of the vertex A.

The coordinates of A are (1,3).

After reflection at

The value of the

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.

Correct answer : (3)

4.

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

a. | glide reflection | ||

b. | rotation | ||

c. | reflection | ||

d. | translation |

L

Figure 2 is the reflected image of Figure 1 in line L

Figure 3 is the reflected image of Figure 2 in line L

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.

Correct answer : (2)

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.

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 |

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.

Correct answer : (1)

6.

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

a. | translation | ||

b. | reflection | ||

c. | rotation | ||

d. | glide reflection |

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>.

Correct answer : (1)

7.

Recognise the design created by glide reflection.

a. | Figure 3 | ||

b. | Figure 4 | ||

c. | Figure 2 | ||

d. | Figure 1 |

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.

Correct answer : (3)

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.

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 |

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.

Correct answer : (4)

9.

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

a. | glide reflection | ||

b. | rotation | ||

c. | translation | ||

d. | reflection |

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

The figure is reflected twice in intersecting lines L

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

Correct answer : (2)

10.

A row of foot prints is an example of which isometry?

a. | reflection | ||

b. | rotation | ||

c. | glide reflection | ||

d. | translation |

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.

Correct answer : (3)