A translation slides every point by the same vector \begin{pmatrix} a \\ b \end{pmatrix}: a units right (left if negative) and b units up (down if negative).
The shape stays the same size and orientation.
Translation by (3, 1)
Reflection
A reflection flips a shape in a mirror line such as x = 2, y = 0 or y = x. Each point is the same distance from the mirror on the opposite side.
Describe it by giving the equation of the mirror line.
Reflection in x = 0
Rotation
A rotation turns a shape about a centre. Give centre, angle and direction, except that a 180° rotation does not need direction.
A 180° rotation gives the same result in either direction.
A quarter-turn about the origin
Enlargement
For enlargement about centre C, image point P′ = C + k(P − C). Distances from C multiply by |k|.
A negative k places corresponding image points on the opposite side of C. For k = −½ the image is smaller, while k = −2 makes it larger. For |k| = 1 size is unchanged.
Enlargement with scale factor 2
Combining and describing
Translation, reflection and rotation give congruent images. Enlargement with nonzero k gives a similar image and is also congruent when |k| = 1.
Give the translation vector, reflection line, rotation centre and angle with direction where needed, or enlargement centre and scale factor.
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1.Which transformation slides a shape without turning it?
Easy
Arotation
Breflection
Ctranslation
Denlargement
2.What is the image of (2, 3) after translation by \begin{pmatrix} 4 \\ 1 \end{pmatrix}?
Easy
A(6, 4)
B(-2, 2)
C(8, 3)
D(5, 7)
3.What is the image of (2, 3) after reflection in the x-axis?
Easy
A(2, -3)
B(-2, 3)
C(-2, -3)
D(3, 2)
4.What is the image of (2, 3) after reflection in the y-axis?
Easy
A(2, -3)
B(-2, 3)
C(-2, -3)
D(3, 2)
5.What is the image of (2, 3) after reflection in y = x?
Easy
A(3, 2)
B(-3, -2)
C(2, -3)
D(-2, 3)
6.What is the image of (2, 3) after a rotation of 180° about the origin?
Easy
A(-2, -3)
B(2, -3)
C(3, 2)
D(-3, 2)
7.What is the image of (2, 0) after a 90° anticlockwise rotation about the origin?
Easy
A(0, 2)
B(0, -2)
C(-2, 0)
D(2, 2)
8.A shape is enlarged by scale factor 3. A side was 4 cm. What is the new side?
Easy
A7 cm
B12 cm
C1.33 cm
D81 cm
もっと問題
9.What does a scale factor of \frac{1}{2} do?
Easy
Aenlarges
Breduces
Creflects
Drotates
10.Point (1, 2) is enlarged by scale factor 3 from the origin. What is the image?
Medium
A(3, 6)
B(4, 5)
C(1, 6)
D(3, 2)
11.Triangle ABC has vertices (1, 1), (3, 1), (1, 4). After enlargement by scale factor 2 from the origin, which is a vertex?
Medium
A(6, 3)
B(2, 2)
C(6, 8)
D(4, 2)
12.Which reflection maps (2, 1) to (−2, 1)?
Medium
Areflection in the y-axis
Breflection in the x-axis
Crotation 90°
Dtranslation
13.What is the mirror line when (3, 4) maps to (5, 4)?
Medium
Ax = 4
By = 4
Cx = 5
Dy = x
14.A rotation of 90° clockwise about the origin maps (0, 3) to:
Medium
A(3, 0)
B(-3, 0)
C(0, -3)
D(0, 3)
15.Which transformation, using scale factor 2 where applicable, gives a similar but non-congruent image?
Medium
Aenlargement
Breflection
Crotation
Dtranslation
16.What is the inverse translation vector for the translation (2, −5)?
Medium
A\begin{pmatrix} -2 \\ 5 \end{pmatrix}
B\begin{pmatrix} 2 \\ 5 \end{pmatrix}
C\begin{pmatrix} 5 \\ -2 \end{pmatrix}
D\begin{pmatrix} -2 \\ -5 \end{pmatrix}
17.Enlarge point (4, 2) by scale factor 2 from centre (1, 1). What is the image?
Medium
A(7, 3)
B(8, 4)
C(5, 3)
D(9, 5)
18.Triangle B is the image of triangle A under enlargement, with corresponding side lengths three times as long and corresponding vertices on the same rays from the centre. What is the scale factor?
Medium
Aenlargement, scale factor 3
Benlargement, scale factor -3
Crotation
Dreflection
19.What is the effect of a negative scale factor of -2?
Medium
Aenlarges on the same side
Benlarges on the opposite side of the centre
Creduces
Dno change
20.Which is a complete description of a 90° rotation?
Medium
Aangle only
Bcentre and angle
Ccentre, angle and direction
Ddirection only
21.What is the order of rotational symmetry of a square?
Easy
A2
B3
C4
D8
22.Under a nonzero translation, which listed property changes?
Easy
Aposition
Bsize
Cangles
Dorientation
23.Under reflection, which is preserved?
Easy
Athe image is congruent
Bthe image is bigger
Cdistance from origin
Dorientation
24.A translation changes the size of a shape.
Easy
True or false?
25.A reflected image is congruent to the object.
Easy
True or false?
26.An enlargement with scale factor 0.5 makes the shape smaller.
Easy
True or false?
27.To describe a 90° rotation fully, you must give its centre, angle and direction.
Easy
True or false?
28.A rotation of 180° clockwise is different from a rotation of 180° anticlockwise.
Medium
True or false?
29.Which transformations produce congruent images?
Medium
Atranslation
Breflection
Crotation
Denlargement scale factor 2
Eenlargement scale factor 1
30.Which are needed to describe an enlargement?
Medium
Acentre
Bscale factor
Cmirror line
Dangle
Evector
31.Describe fully the reflection that maps (2, 3) to (−2, 3) and (4, 1) to (−4, 1).
