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