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