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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.


Correct answer : (4)
 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.


Correct answer : (3)
 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.


Correct answer : (3)
 4.  
Write the ordered pairs in matrix form: A (4, 5), B (2,4), C (- 4, 7)
a.
(4- 425   47)
b.
(   54   7- 42- 4)
c.
(42- 454   7)
d.
(54   742- 4)


Solution:

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



Correct answer : (3)
 5.  
Identify the vertices of quadrilateral PQRS in matrix form.


a.
(- 24321131)
b.
(- 24311132)
c.
(- 21321431)
d.
(- 21143321)


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-coordinate
y-coordinate
(- 21321431)



Correct answer : (3)
 6.  
The matrix (- 5   46   3- 10) 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.
(-1810-154)
b.
(-1   10   8-1- 5- 4)
c.
(-1   8   10-1- 5- 4)
d.
(-1- 5- 4-1   8   10)


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.]


Correct answer : (3)
 7.  
The matrix (- 3- 12   3- 2   21- 1) 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.
(- 1145   0430)
b.
(- 1145   1431)
c.
(- 1145   0431)
d.
(- 1145   2431)


Solution:

Vertices of           Translation Matrix
quadrilateral
(- 3- 12   3- 2   21- 1)    +   (22222222)
[Add 2 to each x-coordinate. Add 2 to each y-coordinate.]

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


Correct answer : (3)
 8.  
The matrix [T] = (- 2 213 41) represents the triangle shown. Identify the transformation applied to obtain the matrix (- 7 -3-48 96).

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.


Correct answer : (4)
 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 quadrilateralTranslation 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).


Correct answer : (3)
 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)


Correct answer : (3)

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