﻿?> Rigid Motion Worksheet | Problems & Solutions

# Rigid Motion Worksheet

Rigid Motion Worksheet
• Page 1
1.
What is the name of the transformation shown?.

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

#### Solution:

A reflection is an isometry which reverses the orientation of a figure.
[Definition.]

2.
What is the name of the transformation shown?

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

#### Solution:

A rotation is an isometry that does not change orientation. Clearly the figure (b) is obtained by rotating the figure (a) through 180° about the point A in the clockwise direction.

3.
The quadrilateral ABCD has undergone through a reflection as shown. Which triangle is congruent to ΔBCD.

 a. Δ GEF b. Δ FGH c. Δ GHE d. Δ FEH

#### Solution:

In the figure shown quadrilateral ABCD has undergone through a reflection about a line. The image of quadrilateral ABCD is quadrilateral EFGH in which Δ BCD is the image of Δ FGH. So ΔBCD Δ FGH.

4.
What is the name of the transformation shown?

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

#### Solution:

Translation is a transformation that moves points, the same distance in the same direction. So the transformation shown is a translation.

5.
Does the transformation appear to be an isometry?

 a. no b. yes c. cannot be determined

#### Solution:

The transformation is not an isometry because the image and pre image are not congruent.

6.
A, B, C, D are points on a line L as shown. If A′ is the reflection of A in line L, then which of the following is correct?

 a. A′ = C b. A′ = A c. A′ = B d. A′ = D

#### Solution:

A is a point on the line L, so its image in line L is itself.
[Definition.]

7.
Name the change in the figure from figure (A) to figure (B).

 a. slide b. rotation c. reflection

#### Solution:

The figure A is rotated 180° to form figure B.

Hence the transformation, that has taken place from figure A to figure B is Rotation.

8.
Name the transformation XUVW $\to$ X′ U′ V′ W′shown.

 a. rotation b. flip c. slide d. turn

#### Solution:

The figure was pulled aside without any alteration in the figure, that is, slided. So, the change is a slide.
[Figure XUVW was transformed to X′ U′ V′ W′, which is a slide.]

9.
Which of the following is the image of the figure ABCD?

 a. EHGF b. HEFG c. EFGH d. GFEH

#### Solution:

The quadrilateral ABCD has undergone through reflection in y-axis. The quadrilateral EFGH is the image of quadrilateral ABCD.

So, the figure ABCD figure EFGH

10.
Transformations that are isometries are called
 a. rigid transformations b. reflections c. rotations d. translations

#### Solution:

The transformations that are isometries are called rigid transformations.
[Definition.]