﻿ Transformations Worksheet | Problems & Solutions # Transformations Worksheet

Transformations Worksheet
• Page 1
1.
Describe the translation of triangle PQR to ACB, if the coordinates of point P are (5, 2) and that of point A are (- 5, 5).  a. Slide ΔPQR 10 units up and 3 units left to get ΔACB. b. Slide ΔACB 3 units up and 10 units left to get ΔPQR. c. Slide ΔPQR 3 units left and 10 units up to get ΔACB. d. Slide ΔPQR 3 units up and 10 units left to get ΔACB.

2.
The point (2, - 8) is first reflected over Y-axis and then reflected over X-axis. What are the coordinates of the final image? a. (- 2, 8) b. (8, - 2) c. (2, 8) d. None of the above

#### Solution:

When a point is reflected over a vertical line, the y-coordinate remains the same and the sign of the x-coordinate changes.

So, the coordinate of the point when reflected over the Y-axis is (- 2, - 8).

When a point is reflected over a horizontal line, the x-coordinate remains the same and the sign of the y-coordinate changes.

So, the coordinates of the point after the reflection on X-axis is (- 2, 8).

3.
Does an equilateral triangle have rotational symmetry? If yes, what is the angle of rotation? a. Yes, 60o b. No c. Yes, 120o d. Yes, 180o

#### Solution:

A figure has rotational symmetry, if the image after a rotation of 180o or less fits exactly on top of the original figure.

If an equilateral triangle is rotated to 120o, the new image exactly fits on the original triangle.

So, an equilateral triangle has rotational symmetry and the angle of rotation is 120o.

4.
Identify the graph that shows the Figure A, rotated through 180° in clockwise direction around the origin.  a. Figure 4 b. Figure 2 c. Figure 1 d. Figure 3

5.
Identify the graph which shows the figure in graph A, rotated through 90° in clockwise direction around the origin.  a. Graph 1 b. Graph 2 c. Graph 4 d. Graph 3

6.
Identify the graph that shows the figure in graph A, rotated through 180° in anti-clockwise direction around the origin.  a. Graph 1 b. Graph 4 c. Graph 3 d. Graph 2

7.
Identify the graph that shows the figure in Graph A, rotated through 90° in clockwise direction around the origin.  a. Graph 5 b. Graph 3 c. Graph 2 d. Graph 1

#### Solution:

A rotation is a transformation that turns a figure about a fixed point called the center of rotation. The following graph is obtained when the figure in Graph A is rotated 90°clockwise direction around the origin.

Therefore, Graph 2 is the correct answer.

8.
Identify the graph that shows the rectangle in Graph A, rotated through 180° in anti-clockwise direction around the origin.  a. Graph 4 b. Graph 1 c. Graph 3 d. Graph 2

9.
Identify the graph that shows the rectangle in Graph A, rotated through 180° in anti-clockwise direction around the origin.  a. Graph 3 b. Graph 2 c. Graph 4 d. Graph 1

#### Solution:

A rotation is a transformation that turns a figure about a fixed point called the center of rotation. The following graph is obtained when the rectangle in Graph A is rotated 180° anti-clockwise direction around the origin.

Therefore Graph 2 is the correct answer.  a. rotation b. reflection c. translation d. cannot be determined