IXL - Sequences of congruence transformations: find the rules (Geometry practice)

Triangle

is the image of triangle

under a translation left 1 unit and down 5 units followed by a reflection.

Write the rules for the translation and reflection.

Translation:

(

)

↦

Reflection:

(

)

↦

ref_doc_title.

Learn with an example

question

Triangle

is the image of triangle

under a rotation

counterclockwise about the origin followed by a translation.

Write the rules for the rotation and translation.

Rotation:

(

)

↦

Translation:

(

)

↦

key idea

The rule for rotating

counterclockwise about the origin is

(

)

↦

(

–

)

The rule for translating h units horizontally and k units vertically is

(

)

↦

(

)

Positive h values move each point right, and negative values move each point left.
Positive k values move each point up, and negative values move each point down.

solution

The first transformation is a rotation

counterclockwise about the origin. Rotate triangle

to get triangle

The rotation rule is

(

)

↦

(

–

)

(

–

)

↦

(

–

)

(

–

)

↦

(

–

)

(

)

↦

(

–

)

The second transformation is a translation. To map triangle

onto

translate

right 6 units. The translation rule is

(

)

↦

(

)

(

–

)

↦

(

–

)

(

–

)

↦

(

–

)

(

–

)

↦

(

)

Looking for more? Try these:

Lesson: Translations

Lesson: Rotations

Lesson: Reflections

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Teacher tools

Work it out

Not feeling ready yet? These can help:

H.13Sequences of congruence transformations: choose the sequence

H.4Translations: write the rule

H.10Reflections and rotations: write the rule

Lesson: Translations

Lesson: Rotations

Lesson: Reflections

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