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TRANSFORMATIONAL MATRICES

Total questions: 82

Worksheet time: 4hrs 5mins

Name
Class
Date
1.

Evaluate the determinant of matrix above.

a)

-9

b)

9

c)

-15

d)

15

2.

Calculate the determinant for the above matrix.

a)

16

b)

-16

c)

-6

d)

6

3.

Given that a system of linear equations are :
x+2y+3z=−5x+2y+3z=-5  
3x+y−3z=43x+y-3z=4  
−3x+4y+7z=−7-3x+4y+7z=-7  
Which of the following is the correct answer to write it into the matrix form , D X = d ?

a)
b)
c)
d)
4.

Find det (D) for the above system of linear equation in matrix form , D X = d.

a)

80

b)

-80

c)

-40

d)

40

5.

Form the matrix   DxD_x   from the system of linear given.

a)
b)
c)
d)
6.

Evaluate the value of det ( DxD_x  ) as given above.

a)

14

b)

-14

c)

-40

d)

40

7.

Form the matrix DyD_y  from the system of linear above.

a)
b)
c)
d)
8.

Evaluate the value of det ( DyD_y  ) as given above.

a)

40

b)

-40

c)

14

d)

-14

9.

FInd the value of det ( DzD_z  ) as given above.

a)

80

b)

-80

c)

-40

d)

40

10.

Find the value of x, y and z by using Cramer's Rule for the system of linear given above.

a)

x = -1 , y = 1 , z = -2

b)

x = 1 , y = 1 , z = 2

c)

x = -1 , y = -1 , z = -2

d)

x = -1 , y = -1 , z = 2

11.

Question no. 3 untill no. 10 is related based on question no. 3.

4 lines
12.

¿Cuál es el nombre de cada entrada de una matriz?

a)

Fila

b)

Dimensión

c)

Elemento

d)

Columna

13.

Identifica la posición del elemento encerrado en un círculo en la matriz

a)

a3,3

b)

a4,3

c)

a3,4

d)

a4,4

14.

¿Cuál es la dimensión de la Matriz D?

a)

2x2

b)

2x3

c)

3x2

d)

Ninguna

15.

En la matriz A ¿Cuál es el elemento a4,2?

a)

-5

b)

8

c)

-2

d)

6

16.

¿Cuál es la dimensión de la Matriz J?

a)

5x2

b)

2x5

c)

6x2

d)

Ninguna

17.

En la matriz C ¿Cuál es el elemento c2,3?

a)

-6

b)

12

c)

-1

d)

13

18.

Si es posible realizar la operación

Suma las matrices

a)
b)
c)
d)

No se puede sumar

19.

Si es posible realiza la operación

Resta las matrices

a)
b)
c)
d)

No se puede restar

20.

Sumar las matrices

a)
b)
c)
d)
21.

Restar las matrices

a)
b)
c)
d)
22.

Sumar las matrices

a)
b)
c)
d)
23.

Restar las matrices

a)
b)
c)
d)
24.

¿Cuál es el nombre de cada entrada de una matriz?

a)

Fila

b)

Dimensión

c)

Elemento

d)

Columna

25.

Identifica la posición del elemento encerrado en un círculo en la matriz

a)

a3,3

b)

a4,3

c)

a3,4

d)

a4,4

26.

¿Cuál es la dimensión de la Matriz D?

a)

2x2

b)

2x3

c)

3x2

d)

Ninguna

27.

En la matriz A ¿Cuál es el elemento a4,2?

a)

-5

b)

8

c)

-2

d)

6

28.

¿Cuál es la dimensión de la Matriz J?

a)

5x2

b)

2x5

c)

6x2

d)

Ninguna

29.

En la matriz C ¿Cuál es el elemento c2,3?

a)

-6

b)

12

c)

-1

d)

13

30.

Si es posible realizar la operación

Suma las matrices

a)
b)
c)
d)

No se puede sumar

31.

Si es posible realiza la operación

Resta las matrices

a)
b)
c)
d)

No se puede restar

32.

Sumar las matrices

a)
b)
c)
d)
33.

Restar las matrices

a)
b)
c)
d)
34.

Sumar las matrices

a)
b)
c)
d)
35.

Restar las matrices

a)
b)
c)
d)
36.
Reflect the point (2, -4) over the y-axis.
a)
(-4, 2)
b)
(-2, 4)
c)
(-2, -4)
d)
(2, 4)
37.

What transformation is happening?

T(x + 2, y - 3)

a)

translate up 2, left 3

b)

translate right 2, up 3

c)

translate right 2, down 3

d)

translate left 3, right 2

38.
Reflect (6, -3) over the line x-axis.
a)
(6, 3)
b)
(-6, -3)
c)
(-3, 6)
d)
(3, -6)
39.
Rotate the point (7,8) around the origin 90 counter clockwise degrees. State the image of the point.
a)
(-7,-8)
b)
(8,-7)
c)
(-8,7)
d)
(8,7)
40.
If you were to rotate ABCD 180°  about the origin, what would the coordinate of A' be?
a)
(-5, 5)
b)
(-3, -5)
c)
(-5, 3)
d)
(-3, 3)
41.

How many degrees COUNTERCLOCKWISE was quadrilateral ABCD rotated?

a)

90°

b)

180°

c)

270°

d)

360°

42.
Determine how to translate triangle ABC to triangle A'B'C'.
a)
(x-2, y+5)
b)
(x+2, y-9)
c)
(x-2, y+9)
d)
(x-9, y+2)
43.
Where would point J' be if you translated point J 5 units to the left and 2 units up?
a)
(5, 3)
b)
(3, -5)
c)
(-5, 3)
d)
(-3, 5)
44.
Which answer shows a reflection across the y-axis?
a)
a
b)
b
c)
c
d)
d
45.

Reflect the point (2, -4) over y = x.

a)
(-4, 2)
b)
(-2, 4)
c)
(-2, -4)
d)
(2, 4)
46.

Reflect the point D (-9, -12) over the line y = -x.

a)

(12, 9)

b)

(-12, -9)

c)

(-12, 9)

d)

(12, -9)

47.

Find the image of F after it has been translated by the vector <5, 1>.

a)

F'( 1, 3)

b)

F' (2, 4)

c)

F' (2, -1)

d)

F' (0, -1)

48.

Find the coordinates of E' after a rotation 90o clockwise.

a)

E' (3, -2)

b)

E' (2, 3)

c)

E' (3, 2)

d)

E' (-3, -2)

49.
Identify the transformation.
a)
Reflection across y-axis
b)
90 Rotation counter clockwise
c)
Translation 5 units left, 1 unit up.
d)
Translation 5 units right, 1 unit down
50.
Write a rule for the translation.
a)
 (x -1, y  + 2)
b)
 (x -2, y  + 1)
c)
 (x +2, y  - 1)
d)
(x +1, y  -  2)
51.
An office supply store sells index cards in two different sizes. The large size is an enlargement of the small size. Both sizes are shown. Find the scale factor of the enlargement.
a)
2
b)
3
c)
4
d)
5
52.
Identify the transformation from ABC to A'B'C'.
a)
90o clockwise rotation
b)
90o counter clockwise rotation
c)
Reflection across the y-axis
d)
Reflection across the x-axis
53.
Which answer shows a reflection across the y-axis?
a)
a
b)
b
c)
c
d)
d
54.
What is the angle of rotation for this counterclockwise rotation about the origin?
a)
90°
b)
180°
c)
270°
d)
360°
55.

Rotation Rules (clockwise):

90o rotation: (x, y)→(y, -x)

What are the coordinates for A' after a 90⁰ rotation clockwise?

a)

(1, 3)

b)

(3, 1)

c)

(3, -1)

d)

(1, -3)

56.
What is Dilation?
a)
Dilation means to enlarge or reduce
b)
Dilation means to reflect on something
c)
Dilation means to like something
d)
Dilation means to make something different by making it smaller
57.

Choose the correct scale factor if the red it the new image

a)

2.5

b)

1.5

c)

3.5

d)

4

58.

What is the term used in geometry that describes a function or object that moves a figure a certain distance and direction

a)

Translation

b)

Reflection

c)

Rotation

d)

Dilation

59.
The point that is to be transformed is called the:
a)
Pre-Image
b)
Image
c)
Post-Image
d)
Transformation
60.

What is a Reflection?

a)

A transformation in which a geometric figure is reflected across a line.

b)

A transformation in which a geometric figure is rotated clockwise or counter-clockwise.

c)

A transformation in which a geometric figure is translate around the graph.

61.
Identify the rule after a 90° counter clockwise rotation:
(x, y) ---> ___________
a)
( y, -x)
b)
( -y, x)
c)
( -x, -y)
d)
( y, -x)
62.

What is a rotation?

a)

When you slide points up/down/left/right.

b)

Depressing...

c)

When the same shape and size, but the figures may be turned in different directions. May be clockwise or counterclockwise.

63.

If point H(–6, 2) is translated 3 units right and 4 units up, what are the coordinates of the translated image?

a)

(-2, 5)

b)

(-3, 6)

c)

(-9, -2)

d)

(-9, 6)

64.

Point N(6, –5) is reflected across the

x-axis. What are the coordinates of the image?

a)

(-6, -5)

b)

(-5, 6)

c)

(5, -6)

d)

(6, 5)

65.

If the figure is rotated 90 degrees clockwise, what are the coordinates of R?

a)

(-3, 3)

b)

(3, -3)

c)

(-3, -3)

d)

(3, 3)

66.

The vertices of triangle GHI are G(1, 2), H(3, 4), and I(4, 2). The triangle will be reflected across the x-axis. What will be the coordinates of the image point H′?

a)

(-3, 4)

b)

(3, -4)

c)

(-3, -4)

d)

(3, 4)

67.

Point W is located at (7, 3) on a coordinate plane. Point W is translated 2 units to the left and 3 units up. What are the coordinates of the image point W′?

a)

(10, 1)

b)

(9, 0)

c)

(5, 6)

d)

(4, 1)

68.

Determine how to translate triangle A'B'C' from triangle ABC.

a)
(x+2, y-5)
b)
(x+2, y-9)
c)
(x-2, y-9)
d)

(x-2, y+9)

69.
Identify the transformation.
a)
Reflection across y axis
b)
Reflection across x-axis
c)
180 Rotation
d)
Translation 2 units down
70.

Describe the transformation:

(x, y) -> (x-2, y+7)

a)

Translation 2 units to the left & 7 units up

b)

Translation 2 units to the left & 7 units down

c)

Translation 2 units to the right & 7 units up

d)

Translation 2 units to the right & 7 units down

71.

Describe the transformation:

(x, y) -> (x, -y)

a)

reflection across the x-axis

b)

reflection across the y-axis

c)

rotation 90 degrees clockwise

d)

rotation 90 degrees counterclockwise

72.

Describe the transformation:

(x, y) -> (-x, y)

a)

reflection across the x-axis

b)

reflection across the y-axis

c)

rotation 90 degrees clockwise

d)

rotation 90 degrees counterclockwise

73.

Describe the transformation:

(x, y) -> (-y, x)

a)

reflection across the x-axis

b)

reflection across the y-axis

c)

rotation 90 degrees clockwise

d)

rotation 90 degrees counterclockwise

74.

Describe the transformation:

(x, y) -> (y, -x)

a)

reflection across the x-axis

b)

reflection across the y-axis

c)

rotation 90 degrees clockwise

d)

rotation 90 degrees counterclockwise

75.
Reflect Point C over the y-axis:
a)
(-3, 2)
b)
(3,2)
c)
(-2,3)
d)
(3,0)
76.
Is the picture being reflected in the y-axis or x-axis?
a)
y-axis
b)
x-axis
77.
If you were to rotate ABCD 90° counterclockwise about the origin, what would the coordinate of A' be?
a)
(-5, 5)
b)
(-3, 5)
c)
(-5, 3)
d)
(-3, 3)
78.
If you were to rotate ABCD 180°  about the origin, what would the coordinate of A' be?
a)
(-5, 5)
b)
(-3, -5)
c)
(-5, 3)
d)
(-3, 3)
79.
Which answer shows a reflection across the y-axis?
a)
a
b)
b
c)
c
d)
d
80.

To slide or move a figure

a)

Translation

b)

Reflection

c)

Rotation

81.

A mirror image of a figure

a)

Translation

b)

Reflection

c)

Rotation

82.

Turning around a point

a)

Translation

b)

Reflection

c)

Rotation

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