IXL | Translations: write the rule

△

is a translation of

△

Write the translation rule.

(

)

↦

–

ref_doc_title.

Learn with an example

question

△

is a translation of

△

Write the translation rule.

(

)

↦

–

key idea

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

The image of the point

(

)

translated

units horizontally and

units vertically is

(

)

is positive the point is translated to the right and if

is negative the point is translated to the left. If

is positive the point is translated up and if

is negative the point is translated down.

Rectangle

is a translation of rectangle

by 10 units to the right and 8 units up.

This translation is described by the rule

(

)

↦

(

)

solution

Since

△

is a translation of

△

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

and

So, look at the pair of corresponding points

and

Now, subtract the

-coordinates

(

–

)

and

(

–

)

to solve for

-coordinate

–

-coordinate

–

(

–

)

Similarly, subtract the

-coordinates

to solve for

-coordinate

–

-coordinate

–

So,

and

–

Therefore, translating

(

–

)

12 units to the right and 8 units down yields

(

–

)

Next, plug

and

–

into the translation formula, and simplify.

(

)

↦

(

)

(

)

↦

Plug in

and

–

(

–

)

Plug in

and

–

(

)

↦

Simplify

(

–

)

Simplify

So, the translation that maps

△

is described by the rule

(

)

↦

(

–

)

Looking for more? Try these:

Lesson: Translations

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Work it out

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R.4Translations: find the coordinates

Lesson: Translations

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