IXL - Rotate polygons about a point (Geometry practice)

Look at this diagram:

Which diagram shows quadrilateral

rotated 30° counterclockwise about

ref_doc_title.

Learn with an example

question

Look at this diagram:

Which diagram shows quadrilateral

rotated 30° counterclockwise about

key idea

Rotations are rigid transformations in which a figure and its image have the same orientation.

△

is a rotation of

△

around the point

△

has the same orientation as

△

Going from

takes you around

△

in a clockwise direction. Similarly, going from

takes you around

△

in a clockwise direction.

To rotate a polygon about a point using a protractor and compass, follow Steps 1-3 for each vertex, then do Step 4.

Step 1: Draw the line segment between the vertex and the point of rotation.
Step 2: Use a protractor to draw the angle of rotation.
Step 3: Use a compass to mark the rotated vertex point on the other side of the angle.
Step 4: Draw line segments connecting the rotated vertices.

solution

To identify the correct diagram, consider the ones where

and

have the same orientation.

Pick a pair of corresponding vertices, such as

and

and consider

and the counterclockwise angle formed by these segments,

∠

In the second diagram,

≅

and

∠

30°

So, the correct answer is:

To check that this is the correct answer, you can construct the rotation.

Since quadrilateral

is rotated 30° counterclockwise about its vertex

the image of

under this rotation is itself.

Therefore, to draw the rotation, follow the three steps for the other three vertices,

and

First, draw the image of

rotated 30° counterclockwise about

Call this point

Step 1-G: Draw the line segment between the vertex and the rotation point.

Draw

Step 2-G: Use a protractor to draw the counterclockwise angle of rotation.

30°

Draw a 30° counterclockwise angle with vertex

and side

Step 3-G: Use a compass to mark the rotated vertex point on the other side of the angle.

30°

Plot

∠

such that

≅

Second, follow the same steps for

to plot

Step 1-I: Draw the line segment between the vertex and the rotation point.

Draw

Step 2-I: Use a protractor to draw the counterclockwise angle of rotation.

30°

Draw a 30° counterclockwise angle with vertex

and side

Step 3-I: Use a compass to mark the rotated vertex point on the other side of the angle.

30°

Plot

∠

such that

≅

Third, follow the same steps for

to plot

Step 1-J: Draw the line segment between the vertex and the rotation point.

Draw

Step 2-J: Use a protractor to draw the counterclockwise angle of rotation.

30°

Draw a 30° counterclockwise angle with vertex

and side

Step 3-J: Use a compass to mark the rotated vertex point on the other side of the angle.

30°

Plot

∠

such that

≅

Step 4: Draw line segments connecting the rotated vertices.

Finally, connect the four vertices

and

to draw the image of quadrilateral

rotated 30° counterclockwise about H.

Looking for more? Try these:

Lesson: Rotations

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	06

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

C.2Angle measures

H.1Classify congruence transformations

Lesson: Rotations

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!