Mathematics for IGCSE & O level - Transformations (Section 2)
1
What is true about the angles after a translation?
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(D)
The angles remain the same.
2
If an object is transformed by a scale factor of 2 and the image is at the same position, how does the object change?
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(C)
It is enlarged.
3
In transformations, what is the 'image'?
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(B)
The result of the transformation.
4
In a reflection, which properties of the object remain the same in the image?
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(B)
Shape and size only.
5
How is the position of the image related to the object after a translation?
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(B)
The image is in a different position.
6
What are the essential characteristics of a single transformation?
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(A)
Only one type of transformation.
7
Which of the following is a rigid transformation?
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A
B
D
8
What is the centre of enlargement in a shape enlarged by scale factor k=2? (center is located at point (1,1) )
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(A)
(1,1)
9
Which of the following transformations results in an image that is the same size and shape as the original object, but in a different position?
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(D)
all of the above
10
What does an enlargement with a scale factor greater than 1 do to a shape?
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(D)
It enlarges the shape.
11
What is the difference between a rotation and a reflection?
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(C)
A reflection reverses the orientation, a rotation does not.
12
Which transformation does NOT alter the shape of the original figure?
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(B)
Reflection
13
What happens to the coordinates of a point during a reflection across the y-axis?
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(A)
The x-coordinate changes sign.
14
What are the characteristics of an isometry?
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(C)
It preserves distance.
15
What happens when a point is reflected over the line y = x?
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(B)
The x and y coordinates switch places.
16
Which of the following describes the transformation that is equivalent to a rotation of 90° clockwise about the origin, followed by a reflection in the line y = x?
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(D)
A combination of transformations
17
A shape is rotated 180 degrees about a point. Which of the following is true about the image and the original shape?
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(A)
The image is the same size but in a different position.
18
In a translation, what changes about the object's position?
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(D)
Location
19
What does the center of rotation determine in a rotation?
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(B)
The point around which the object turns.
20
In an enlargement, what is the role of the scale factor?
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(B)
To change the size of the object
21
Which transformation does NOT change the area of the shape?
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(B)
Translation
22
If a triangle has vertices A(1, 1), B(1, 3), and C(3, 1), what are the vertices of the image after a reflection in the line y=x?
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(A)
A'(1, 1), B'(3, 1), C'(1, 3)
23
If the scale factor is less than 1, what happens to the image?
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(B)
The image gets smaller.
24
What are two important things about an enlargement?
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A
B
25
Which transformation changes the size of a shape?
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(D)
Enlargement
26
In the context of transformations, what does 'orientation' refer to?
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(C)
The way the object is 'facing'.
27
Which of these is not preserved in an enlargement?
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(D)
Size
28
If a point is rotated 270 degrees counterclockwise about the origin, what are the new coordinates?
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(A)
(y, -x)
29
Which of the following transformations change the size of the object?
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(D)
Enlargement
30
Which of the following statements is correct about Enlargement?
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A
B
31
Which of the following must be the same to describe a single transformation?
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A
B
C
32
If the coordinates of a point are (3, -2), and it is enlarged by a scale factor of 2, what are the new coordinates (assuming center of enlargement is the origin)?
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(C)
(6, -4)
33
In a reflection, what do we call the line that acts as a mirror?
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(A)
Mirror line
34
A point with coordinates (5, -3) is reflected in the x-axis. What are the new coordinates?
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(B)
(5, 3)
35
Which of the following transformations maintains the shape of a geometric figure?
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(D)
All of the above
36
What remains unchanged in a reflection?
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(D)
Shape
37
If a shape is translated using the vector $\begin{pmatrix} 0 \ -5 \end{pmatrix}$, what happens to its position?
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(B)
The shape moves 5 units down.
38
Which transformation will always result in a change of size?
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(D)
Enlargement (except with a scale factor of 1)
39
Which transformation involves a center of rotation?
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(C)
Rotation
40
What happens to the image if the scale factor of an enlargement is negative?
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(A)
The image is inverted on the opposite side of the center of enlargement from the object.
41
If a shape is translated by the vector <2, -3>, how does the shape change?
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(B)
It moves 2 units right and 3 units down.
42
If a point is translated by the vector <0, 4>, what will happen?
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(C)
The point moves 4 units up.
43
In a rotation, all the points move through the same angle about the same...
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(B)
Centre
44
If the scale factor is negative, what is the effect on the object in an enlargement?
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(B)
The image is inverted.
45
What is the result if we double the size of the image?
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(A)
Enlargement with scale factor 2.
46
If a point is reflected across the y-axis, how do the coordinates change?
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(A)
(x, y) becomes (-x, y)
47
Which transformation(s) will always produce congruent images?
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A
C
D
48
If a figure is translated, how do its properties change?
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(B)
The shape and size remain the same.
49
In an enlargement, how is the image related to the original object?
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(C)
The image's shape is preserved and it may change in size
50
If a figure is rotated 90 degrees counterclockwise, about the origin, what are the rules of the transformation?
