Geometry Chapter 4 Review

-Rotations

-Translations

-Reflections

-Dilations

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Chapter 4: Transformations

rotation

turn a figure
about a point,
called the center
of rotation

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Multiple Choice

Point A is located at (4,-7). The point is reflected rotated 180° CW. Its image is located at...

• (-4, 7)

• (-4, -7)

• (4, 7)

• (7, -4)

Multiple Choice

Rotate the point (-5,8) around the origin 270 degrees counterclockwise. State the image of the point.

• (-8,5)

• (8,-5)

• (8,5)

• (5,-8)

Multiple Choice

Triangle C is rotated 180° clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A

• B

• C

• D

translation

slide a figure
without turning it

Multiple Choice

Triangle ABC has vertices at A(6, 1) B(1, 7) and C(-3, -2). The translation to create triangle A'B'C' is (x, y) goes to (x - 1, y + 2). Which will be the coordinates of triangle A'B'C'?

• A'(5, 2), B'(0, -4), C'(0, 9)

• A'(5, 3), B'(0, -4), C'(0, 8)

• A'(5, 3), B'(0, 9), C'(-4, 0)

• A'(5, 2), B'(1, -3), C'(0, 9)

Multiple Choice

Determine where X' would be if you translated X 3 units to the left and 9 units down.

• (-4, 4)

• (-10, 2)

• (-4, -5)

• (-1, 5)

reflection

place point on the
opposite side of a
reflection line

Multiple Choice

What is a reflection?

• When you turn an object around a point.

• When you slide an object form one place to another.

• When you flip or mirror an object across a line.

• When you resize an object.

Multiple Choice

State the line of reflection.

• Reflection across y-axis

• Reflection across x-axis

• Reflection across x = 1

• Reflection across y = 1

Multiple Choice

Which answer shows a reflection across the x-axis?

• d

• c

• b

• a

Multiple Choice

If A(2,5) was reflected over the Y-AXIS, what would the coordinated of A' be?

• A'(2,-5)

• A'(-2,5)

• A'(5,2)

• A'(5,-2)

Multiple Choice

Triangle GHI is reflected across the x-axis.  What are the coordinates of I'?

• (-2, 6)

• (2, 6)

• (-6, -2)

• (6, 2)

​Key Concepts:

• A DILATION stretches of shrinks a figure.

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• The CENTER OF DILATION never changes position. It is the starting point.

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• ​The SCALE FACTOR tells you how much the dilation stretches or shrinks.

A DILATION is a transformation that produces an image that is the same shape as the pre-image, but is a different size. Dilations create similar figures. 

• Scale factor is greater than 1​

• Image gets BIGGER​

Enlargement

• Scale factor is less than 1​

• ​Image gets SMALLER

​​Reduction

Multiple Choice

First, identify the old and new image. Now, did the triangle get bigger or smaller?

• The triangle got smaller

• The triangle got bigger

Multiple Choice

First, identify the old and new image. Now, did the triangle get bigger or smaller?

• The triangle got smaller

• The triangle got bigger

Multiple Choice

Is this an enlargement or a reduction?

• Enlargement

• Reduction

Multiple Choice

Is this an enlargement or a reduction?

• Enlargement

• Reduction

Multiple Choice

The two rectangles are scale drawings. What is the measurement of x?

• 21

• 1.25

• 20

• 4

Multiple Choice

Dilate Point B by a scale factor of 3:

• (12,0)

• (12,12)

• (4,3)

• (0,12)

​Multiply all the coordinate numbers by 3.

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Vertex A (4,-2), A' (12, -6)

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Vertex B (-2,-2), B' (-6, -6)​

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Vertex C (-2,2)​, C' (-6, 6)

​Draw the dilation of triangle ABC, with center (0,0), and scale factor 3. Label this triangle A'B'C'.

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Multiple Choice

Apply a dilation of triangle ABC, with center (0,0), and scale factor 2.

A' will be at ...

• (8,-4)

• (2,2)

Multiple Choice

Apply a dilation of triangle ABC, with center (0,0), and scale factor 1/2.

A' will be at ...

• (-4,4)

• (-2,-1)