IXL | Translations: write the rule

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or

Learn with an example

question

△

E'

F'

G'

is a translation of

△

EF

G

.

Write the translation rule.

(

x

,

y

)

↦

x

–

,

y

–

key idea

A translation shifts each point the same distance horizontally and the same distance vertically.

The image of the point

(

x

,

y

)

translated

h

units horizontally and

k

units vertically is

(

x

+

h

,

y

+

k

)

.

If

h

is positive the point is translated to the right and if

h

is negative the point is translated to the left. If

k

is positive the point is translated up and if

k

is negative the point is translated down.

Rectangle

A'

B'

C'

D'

is a translation of rectangle

A

B

C

D

by 10 units to the right and 8 units up.

This translation is described by the rule

(

x

,

y

)

↦

(

x

+

10

,

y

+

8

)

.

solution

Since

△

E'

F'

G'

is a translation of

△

EF

G

,

you only have to use one pair of corresponding vertices to solve for

h

and

k

.

So, look at the pair of corresponding points

F

and

F'

.

Now, subtract the

x

-coordinates

of

F

(

7

,

9

)

and

F'

(

–

1

,

–

2

)

to solve for

h

.

h

=

x

-coordinate

of

F'

–

x

-coordinate

of

F

=

–

1

–

7

=

–

8

Similarly, subtract the

y

-coordinates

to solve for

k

.

k

=

y

-coordinate

of

F'

–

y

-coordinate

of

F

=

–

2

–

9

=

–

11

So,

h

=

–

8

and

k

=

–

11

.

Therefore, translating

F

(

7

,

9

)

8 units to the left and 11 units down yields

F'

(

–

1

,

–

2

)

.

Next, plug

h

=

–

8

and

k

=

–

11

into the translation formula, and simplify.

(

x

,

y

)

↦

(

x

+

h

,

y

+

k

)

(

x

,

y

)

↦

Plug in

h

=

–

8

and

k

=

–

11

(

x

+

–

8

,

y

+

–

11

)

Plug in

h

=

–

8

and

k

=

–

11

(

x

,

y

)

↦

Simplify

(

x

–

8

,

y

–

11

)

Simplify

So, the translation that maps

△

EF

G

to

△

E'

F'

G'

is described by the rule

(

x

,

y

)

↦

(

x

–

8

,

y

–

11

)

.

Looking for more? Try these:

Lesson: Translations

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