IXL | Sequences of congruence transformations: graph the image

Graph the image of

△

after the following sequence of transformations:

Rotation

180

counterclockwise around the origin

Translation 1 unit left and 21 units down

Coordinate plane graph with 4 quadrants, x-axis coordinates from -15 to 15, y-axis coordinates from -15 to 15. The following data are shown. Point (9, -14). Point (6, -8). Point (3, -14).

ref_doc_title.

Learn with an example

question

Graph the image of

△

after the following sequence of transformations:

Rotation

counterclockwise around the origin

Translation 17 units right and 19 units down

key idea

The image of a point

(

)

rotated

counterclockwise around the origin is

(

–

)

The image of a point

(

)

translated h units right and k units down is

(

–

solution

First, rotate

△

counterclockwise around the origin. Use the transformation rule

(

)

↦

(

–

)

to find the image of each of its three vertices.

(

)

↦

(

–

)

(

)

↦

(

–

)

(

)

↦

(

–

)

Second, translate

△

To translate the triangle 17 units right and 19 units down, use the transformation rule

(

)

↦

(

–

)

to find the image of each of its three vertices.

(

–

)

↦

(

–

)

(

–

)

↦

(

–

)

(

–

)

↦

(

–

)

So, the image of

△

after rotating

counterclockwise around the origin and translating 17 units right and 19 units down is

△

Looking for more? Try these:

Lesson: Transformations

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Teacher tools

Work it out

Not feeling ready yet? These can help:

R.10Rotations: graph the image

R.6Reflections over the x- and y-axes: graph the image

R.3Translations: graph the image

Lesson: Transformations

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