Topics
13. Coordinate Geometry
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iGCSE (2021 Edition)

13.04 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, describe the translation from figure A to figure B:

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
Rotations
25

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
26

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
27

Consider the following shape:

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

1
2
3
4
5
6
7
8
9
10
11
x
1
2
3
4
5
6
7
8
9
10
11
y
28

Consider the shape shown:

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

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
29

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
30

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
31

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
32

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

0580C3.1

Demonstrate familiarity with Cartesian coordinates in two dimensions.

0580E3.1

Demonstrate familiarity with Cartesian coordinates in two dimensions.

0580C7.2

Reflect simple plane figures in horizontal or vertical lines. Rotate simple plane figures about the origin, vertices or midpoints of edges of the figures, through multiples of 90°. Construct given translations and enlargements of simple plane figures. Recognise and describe reflections, rotations, translations and enlargements.

0580E7.2

Reflect simple plane figures. Rotate simple plane figures through multiples of 90°. Construct given translations and enlargements of simple plane figures. Recognise and describe reflections, rotations, translations and enlargements.

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