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