IXL | Sequences of congruence transformations: graph the image

Graph the image of

△

after the following sequence of transformations:

Reflection across the

-axis

Rotation

counterclockwise around the origin

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 (-6, 11). Point (-3, 5). Point (3, 8).

ref_doc_title.

Learn with an example

question

Graph the image of

△

after the following glide reflection:

Translation 14 units down

Reflection across the

-axis

key idea

A glide reflection is the composition of a translation followed by a reflection across a line parallel to the direction of the translation.

The image of a point

(

)

translated k units down is

(

–

The image of a point

(

)

reflected across the

y-axis

(

–

)

solution

First, translate

△

To translate the triangle 14 units down, use the transformation rule

(

)

↦

(

–

)

to find the image of each of its three vertices.

(

–

)

↦

(

–

)

(

–

)

↦

(

–

)

(

–

)

↦

(

–

)

Second, reflect

△

across the

-axis.

Use the transformation rule

(

)

↦

(

–

)

to find the image of each of its three vertices.

(

–

)

↦

(

–

)

(

–

)

↦

(

–

)

(

–

)

↦

(

–

)

So, the image of

△

after translating 14 units down and reflecting across the

-axis

△

Looking for more? Try these:

Lesson: Transformations

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Teacher tools

Work it out

Not feeling ready yet? These can help:

EE.8Rotations: graph the image

EE.4Reflections over the x- and y-axes: graph the image

EE.2Translations: graph the image

Lesson: Transformations

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