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Mathematics for IGCSE & O level - Transformations (Section 6)

1
If a shape undergoes a rotation of 180 degrees, what changes about the coordinates?
Answer
(C)
(x, y) becomes (-x, -y)
2
What is the effect of a scale factor of 1 on an enlargement?
Answer
(C)
The object remains the same size.
3
What is the key difference between an enlargement and a translation?
Answer
(A)
Enlargement changes size, translation does not.
4
What does a negative scale factor indicate in an enlargement?
Answer
(C)
The object is reflected and resized.
5
When a shape is reflected over the y-axis, the coordinates transform by:
Answer
(A)
(x, y) -> (-x, y)
6
When reflecting a point (x, y) across the line y = -x, what happens to the coordinates?
Answer
(B)
(x, y) becomes (-y, -x)
7
If a transformation is followed by another, what should you do?
Answer
(B)
Perform the transformations in the order specified in the problem.
8
A shape is reflected across the line y=x. Which of the following is true about the original shape and its image?
Answer
(A)
The shape and its image are congruent.
9
What is the scale factor if the image is half the size of the original object?
Answer
(A)
1/2
10
In an enlargement, where is the image relative to the object when the scale factor is greater than 1?
Answer
(B)
Larger than the object
11
When the scale factor is positive, which side will the image be?
Answer
(A)
The same side as the original shape.
12
Which transformation always results in a congruent image?
Answer
A
B
C
13
Which transformation preserves the size and shape of the original figure?
Answer
(C)
Translation
14
In a reflection, what acts as the 'mirror'?
Answer
(B)
The line of reflection
15
What is the effect of multiplying the coordinates of a point (x, y) by a scale factor?
Answer
(C)
Enlargement or reduction relative to the origin.
16
Which transformation(s) result in a congruent image?
Answer
B
C
D
17
What is the key to identify a translation transformation?
Answer
(B)
The shape moves without turning or turning round.
18
Which of the following is correct about a rotation transformation?
Answer
A
C
19
Which type of transformation always changes the size of the figure?
Answer
(D)
Enlargement
20
Which of the following is a characteristic of a rotation?
Answer
(B)
The shape turns around a fixed point and the size remains the same.
21
If a shape is enlarged with a scale factor of 1/2, is the image smaller or larger?
Answer
(B)
Smaller
22
What transformation is represented by a vector in a coordinate plane?
Answer
(C)
Translation
23
Which transformation would produce an image that is smaller than the original object?
Answer
(C)
Enlargement with a scale factor between 0 and 1
24
In a reflection across the x-axis, the y-coordinate:
Answer
(B)
Changes sign
25
Which transformations result in congruent images?
Answer
A
B
C
26
If the scale factor of an enlargement is between 0 and 1, what happens to the image?
Answer
(B)
It becomes smaller than the object.
27
In a rotation, which of the following factors do you need to know?
Answer
A
B
C
28
In which type of transformation does the object and its image have the same orientation?
Answer
A
B
29
What happens when a figure is reflected in the line y = -x?
Answer
(B)
(x, y) becomes (y, x)
30
When dealing with an enlargement, what is the purpose of the center of enlargement?
Answer
(C)
To find the point from which the shape is scaled.
31
What characterizes the image after a reflection?
Answer
(B)
It is congruent to the original
32
Which transformation(s) does not change the distance between any two points on a figure?
Answer
A
B
C
33
If a shape is rotated 180 degrees about the origin, which of the following transformations occur?
Answer
(D)
The x and y coordinates switch and change sign.
34
If a shape is translated by the vector <-4, 1>, what does this mean for the coordinates of a point on the shape?
Answer
(D)
Move 4 units left and 1 unit up
35
What is the relationship between the original shape and its image in an enlargement?
Answer
(B)
They are similar.
36
What must be specified to fully describe a rotation?
Answer
(C)
Center of rotation and angle of rotation
37
What type of transformation is used when a figure is moved along a straight line without any rotation or reflection?
Answer
(C)
Translation
38
Which of the following describes a reflection?
Answer
(B)
The shape's size is the same as the image.
39
If you reflect a point across the x-axis, what happens to its coordinates?
Answer
(B)
(x, y) becomes (x, -y)
40
When a figure is rotated, which point typically remains fixed?
Answer
(C)
The center of rotation
41
In the context of transformations, what does 'congruent' mean?
Answer
(A)
Having the same size and shape
42
Which of the following is NOT a type of transformation?
Answer
(C)
Division
43
A transformation in which the image is similar to the pre-image is called a:
Answer
(D)
Dilation
44
In what type of transformation does the shape's orientation change, but not the size?
Answer
(C)
Reflection
45
What are some defining characteristics of enlargement transformations?
Answer
A
C
46
What is the scale factor of a reduction?
Answer
(C)
Between 0 and 1
47
If a point is translated by a vector <3, -2>, what is happening to the point?
Answer
(B)
The point is moving 3 units to the right and 2 units down.
48
How can you check if a single transformation is a rotation?
Answer
(C)
Measure the angles between corresponding sides.
49
When is an enlargement considered the same size?
Answer
(C)
The scale factor is 1.
50
What factor determines whether the enlargement becomes larger or smaller?
Answer
(C)
The scale factor.