Topics
11. Coordinate Geometry
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iGCSE (2021 Edition)

11.03 Transformations

Lesson
Worksheet
Practice
Worksheet
Translations
1

State the type of transformattion that has occured on the following shapes:

a
b
c
2

Translate the given flag 1 unit up and 2 units to the right on the number plane:

1
2
3
4
x
1
2
3
4
y
3

For each of the following points, plot the translated point using the given instruction:

a

Translate the point 3 units to the right.

-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
b

Translate the point 4 units to the left.

-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
c

Translate the point 7 units up.

-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
d

Translate the point 4 units down.

-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
e
Translate the point 2 units to the right and 4 units down.
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
f

Translate the point 5 units to the left and 6 units up.

-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
4

For each of the following graphs:

i

Describe the translation from figure A to figure B.

ii

Describe the inverse translation from figure B to figure A.

a
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
y
b
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
y
c
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
y
d
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
9
10
y
e
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
y
f
1
2
3
4
5
6
7
8
9
10
x
1
2
3
4
5
6
7
8
y
g
1
2
3
4
5
6
x
1
2
3
4
5
6
7
8
y
h
1
2
3
4
5
6
7
x
1
2
3
4
5
6
7
8
y
5

For each of the following, describe the translation from figure B to figure A:

a
1
2
3
4
5
6
7
8
9
x
1
2
3
4
5
y
b
1
2
3
4
5
6
7
8
9
x
1
2
3
4
5
6
7
y
c
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
9
y
d
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
9
10
11
y
e
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
y
f
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
y
g
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
9
10
11
y
h
1
2
3
4
5
6
7
x
1
2
3
4
5
6
y
6

For each of the following, describe the translation of triangle ABC to triangle A'B'C':

a
-3
-2
-1
1
2
3
4
5
6
7
8
9
x
1
2
3
4
5
6
y
b
-1
1
2
3
4
5
6
7
x
1
2
3
4
5
6
7
8
9
y
c
-6
-4
-2
2
4
6
8
10
x
1
2
3
4
5
6
7
8
9
y
7

For each of the following, describe the translation of the trapezium ABCD to the trapezium A'B'C'D':

a
-4
-3
-2
-1
1
2
3
4
5
6
x
1
2
3
4
5
6
7
8
9
10
y
b
-4
-3
-2
-1
1
2
3
4
x
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
y
c
-8
-6
-4
-2
2
4
6
x
-10
-8
-6
-4
-2
2
4
y
8

For each of the following, describe the translation of the polygon A to the polygon B:

a
-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
y
b
-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
y
c
-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
y
9

A point has been translated 2 units left. The translated point is shown on the right. Plot the starting position of this point before it was translated.

1
2
3
4
5
6
7
8
9
x
1
2
3
4
5
6
7
8
9
y
10

A triangle has been translated 3 units left. The translated triangle is shown on the right. Plot the starting position of the triangle before it was translated.

1
2
3
4
5
6
7
8
9
x
1
2
3
4
5
6
7
8
9
y
11

The point on the number plane is translated 4 units up. Write down the coordinates of its new position.

-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
12

Point A is translated 3 units down and 4 units to the right, where it sits at point \left(5, - 2 \right). Write down the coordinate of the original point A.

Reflections
13

State the type of transformation that has occured on the following shapes:

a
b
c
d
14

True or false:

A shape is reflected across a line. If the reflected shape is then reflected across the same line again, it will return to the original shape.

15

Determine whether the following diagrams show a reflection across the given line:

a
1
2
3
4
5
6
7
8
9
x
1
2
3
4
5
6
7
8
9
y
b
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
y
c
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
y
d
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
y
e
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
y
16

Reflect the following shapes about the given line:

a
b
c
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
17

The square below is reflected about the given line. Which point would correspond to point A?

18

For each of the following:

  • Plot the point A on a number plane.

  • Plot point A', a reflection of point A across the indicated axis.

a

A \left(8,5\right) \, ; \, x-axis

b

A \left(-10,-6\right) \, ; \, x-axis

c

A \left(-5,-3\right) \, ; \, y-axis

d

A \left(8,-6\right) \, ; \, y-axis

19

Consider the point A \left(5, 6\right).

a

Plot point A on a number plane.

b

If point A is reflected across the y-axis to produce point B, what will be the coordinates of point B?

c

What distance would the original point A need to be translated to overlap point B?

20

Consider the line segment AB, where the endpoints are A \left( - 9 , - 10 \right) and B \left(4, 3\right).

a

Plot the line segment AB on a number plane.

b

Plot the reflection of the line segment AB across the x-axis.

21

Plot the reflection of the given triangle across the line x = 3:

-2
-1
1
2
3
4
5
6
7
8
x
-10
-8
-6
-4
-2
2
4
6
y
22

Plot the reflection of the given triangle across the line y = 3:

-8
-6
-4
-2
2
4
6
8
x
-4
-2
2
4
6
8
y
23

Plot the reflection of the given triangle across the line x = - 3:

-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
x
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
y
24

Plot the reflection of the given triangle across the line y = -1:

-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
y
25

Describe the inverse transformation for each of the following transformations:

a

Reflection across the x-axis.

b

Reflection across the y-axis.

c

Reflection across the line y=x.

d

Reflection across the line x=3.

Rotations
26

Find the coordinates of point B when it is rotated 90 \degree clockwise about the origin.

-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
27

Consider the flag on the number plane shown:

Draw the flag after it has been rotated:

a

90 \degree about point A.

b

180 \degree about point A.

c

270 \degree about point A.

1
2
3
4
5
x
1
2
3
4
5
y
28

Consider the following shape:

a

Draw the shape after it has been rotated by 180 \degree clockwise about point A.

b

Describe the inverse transformation.

1
2
3
4
5
6
7
8
9
10
11
x
1
2
3
4
5
6
7
8
9
10
11
y
29

Consider the shape shown:

a

Draw the shape after it has been 135 \degree anticlockwise rotated about point A.

b

Describe the inverse transformation.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
x
1
2
3
4
5
6
7
8
9
10
11
12
13
y
30

Which shape corresponds to a rotation of triangle R by 270 \degree clockwise about the origin?

-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
31

Suppose all four triangles in the image below are rotated 270 \degree clockwise about the origin.

Which image would correspond to the result of this transformation?

-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
A
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
B
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
C
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
D
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
32

For each of the following:

i

Find the clockwise angle of rotation of shape A to shape B about point O.

ii

Find the anticlockwise angle of rotation of shape A to shape B about point O.

a
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
y
b
1
2
3
4
5
6
7
x
1
2
3
4
5
6
7
8
9
y
33

Consider the following image:

a

Which segment represents a clockwise rotation of segment PQ by 90 \degree about point O?

b

Which segment represents an anticlockwise rotation of segment XY by 270 \degree about point O?

1
2
3
4
5
6
7
8
9
10
11
x
1
2
3
4
5
6
7
8
9
10
11
y
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Outcomes

0607C6.4

Transformations on the Cartesian plane: translation, reflection, rotation, enlargement (reduction). Description of a transformation.

0607E6.4

Transformations on the Cartesian plane: translation, reflection, rotation, enlargement (reduction). Description of a transformation.

0607E6.5

Inverse of a transformation.

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