﻿ Transformations with Matrices Worksheet | Problems & Solutions

# Transformations with Matrices Worksheet

Transformations with Matrices Worksheet
• Page 1
1.
Which of the transformations is applied on the rectangle 1 to obtain the rectangle 2?

 a. Dilation b. Reflection c. Translation d. Rotation

#### Solution:

Rectangle 1 is turned through an angle of 90o to get rectangle 2 about the point P.

The transformation is rotation.

2.
Describe the transformation for the figures (1) and (2).

 a. Dilation b. Translation c. Reflection d. Rotation

#### Solution:

y-axis is the axis of symmetry for the figures (1) and (2).

The transformation is reflection.

3.
What is the transformation from figure 1 to figure 2?

 a. Translation b. Reflection c. Dilation d. Rotation

#### Solution:

Figure 1 is enlarged by a scale factor of 2. The transformation from figure 1 to figure 2 is dilation.

4.
Write the ordered pairs in matrix form: A (4, 5), B (2,4), C (- 4, 7)
 a. b. c. d.

#### Solution:

A   B   C
 x-coordinatey-coordinate (42- 454   7)

5.
Identify the vertices of quadrilateral PQRS in matrix form.

 a. $\left(\begin{array}{cccc}- 2& 4& 3& 2\\ 1& 1& 3& 1\end{array}\right)$ b. $\left(\begin{array}{cccc}- 2& 4& 3& 1\\ 1& 1& 3& 2\end{array}\right)$ c. $\left(\begin{array}{cccc}- 2& 1& 3& 2\\ 1& 4& 3& 1\end{array}\right)$ d. $\left(\begin{array}{cccc}- 2& 1& 1& 4\\ 3& 3& 2& 1\end{array}\right)$

#### Solution:

The vertices of quadrilateral PQRS are

P (- 2, 1), Q (1, 4), R (3, 3) and S (2, 1)

P   Q   R    S
 x-coordinatey-coordinate (- 21321431)

6.
The matrix represents the vertices of a triangle. Translate 4 units right and 4 units down and choose the vertices of the image as a matrix.
 a. $\left(\begin{array}{ccc}-1& 8& 10\\ -1& 5& 4\end{array}\right)$ b. c. d.

#### Solution:

Vertices of triangle  Translation matrix
(- 5   46   3- 10)     +    (   4   4   4- 4- 4- 4)
[Add 4 to each x co-ordinate. Subtract 4 from each y coordinate.]

= (-1   8   10-1- 5- 4)
[Vertices of the image in matrix form.]

7.
The matrix represents the vertices of a quadrilateral. Translate 2 units right and 2 units up and choose the vertices of the image as a matrix.
 a. b. c. d.

#### Solution:

Vertices of           Translation Matrix
(- 3- 12   3- 2   21- 1)    +   (22222222)

= (- 1145   0431)
[Vertices of the image in matrix form.]

8.
The matrix [T] = $\left(\begin{array}{ccc}- 2& 2& 1\\ 3& 4& 1\end{array}\right)$ represents the triangle shown. Identify the transformation applied to obtain the matrix $\left(\begin{array}{ccc}- 7& -3& -4\\ 8& 9& 6\end{array}\right)$.

 a. translation of 5 units right and 5 units down b. a translation of 5 units left and 5 units down c. a translation of 5 units right and 5 units up d. a translation of 5 units left and 5 units up

#### Solution:

[T] = (- 2 213 41).
[Given.]

(- 7 -3-48 96) - (- 2 213 41) = (-5-5-5555)

Therefore, a translation of 5 units left and 5 units up describes the translation.

9.
Find the coordinates of the image of the quadrilateral ABCD under a translation of 4 units right and 3 units down.

 a. (6, 4), (4, - 6), (8, - 8), (9, - 5) b. (- 6, - 4), (- 4, - 6), (8, - 8), (9, - 5) c. (6, - 4), (4, - 6), (8, - 8), (9, - 5) d. (6, 0), (4, -2), (8, 8), (9, -1)

#### Solution:

Vertices of the quadrilateral ABCD are (2, - 1), (0, - 3), (4, - 5), (5, - 2)

 Vertices of quadrilateral Translation matrix (   2   0   4   5- 1- 3- 5- 2)  + (   4   4   4   4- 3- 3- 3- 3)

[Add 4 to each x-coordinate. Subtract 3 from each y-coordinate.]

= (  6  4  8  9- 4- 6- 8- 5)

Therefore, vertices of the image of the quadrilateral ABCD are (6, - 4), (4, - 6), (8, - 8), (9, - 5).

10.
Identify the matrix that represents the vertices of graph $f$ and graph $g$.

 a. I b. IV c. III d. II

#### Solution:

The vertices of graph f are (- 2, 4), (- 2, 1), (3, 1)

The vertices of graph g are (2, 4), (2, 1), (7, 1)

Therefore, f: (- 2- 23411), g: (227411)