Rules for Reflection Geometry

Reflections

by Sydney Elkin

​What is a reflection?

​A reflection is a type of transformation that "flips" an image.

​

​Because the pre-image and image are congruent, reflections are rigid motions.

​

Multiple Choice

What type of transformation is the image to the left?

• Translation

• Reflection

• Neither

​Some reflections have definite rules

• ​Across the x-axis

• ​Across the y-axis

• ​Across the line y=x

• ​Across the line y=-x

Multiple Choice

• y-axis

• x-axis

• y=x

• y=-x

Multiple Choice

• y-axis

• x-axis

• y=x

• y=-x

Multiple Choice

• y-axis

• x-axis

• y=x

• y=-x

Multiple Choice

• y-axis

• x-axis

• y=x

• y=-x

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Topics You Need to Know

1. ​Reflections are rigid motions

2. ​Reflections can take place over either axis or any line

3. ​​Reflections over the y-axis, x-axis, y=x or y=-x all have specific rules

4. ​The line of reflection is a perpendicular bisector of any segment connecting a point in the pre-image to its corresponding point in the image

5. ​If a point in the pre-image and image are the same, then it lies on the line of reflection.

Multiple Choice

Is the picture being reflected in the y-axis or x-axis?

• y-axis

• x-axis

Multiple Choice

Reflect a figure over the y-axis- 

• Change the x-coordinate

• Change the y-coordinate

Multiple Choice

Reflect a figure over the x-axis- 

• Change the x-coordinate

• Change the y-coordiate

Multiple Choice

Describe the transformation shown in the graph.

• Reflect over x-axis

• Reflect over y-axis

• Rotate 180 degrees

• Translate 4 units right

Multiple Choice

Describe the transformation shown on the graph.

• Reflect over x-axis

• Reflect over y-axis

• Rotate 180 degrees

• Rotate 90 degrees CCW

Multiple Choice

What is this transformation? (x, y) ----> (-x, y) 

• Reflect over the x axis

• Reflect over the y-axis

• Slide down 1

• slide left 1

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

How do you represent a translation Algebraically? 

• (-y, -x)

• (x + a, y + b)

• (-x , -y)

• (ax, by)

Multiple Choice

What is the algebraic representation of translating a figure 4 units down?

• (x-4, y-4)

• (x, y-4)

• (x-4, y)

• (x+4, y+4)

Multiple Choice

A slide is also called a _________.

• Translation

• Reflection

• Rotation

• Transformation

Multiple Choice

A turn is also called a ___________.

• Translation

• Reflection

• Rotation

• Transformation

Multiple Choice

Name the transformation.

• Translation

• Reflection

• Rotation

Multiple Choice

Describe the Transformation

• Translation

• Reflection

• Rotation

Multiple Choice

What Transformation is visible?

• Reflection

• Rotation

• Dilation

• Translation

Multiple Choice

After being transformed the new point is called a(n):

• Pre-Image

• Post Image

• Transformed

• Image

Multiple Choice

If you reflect point (-2,7) over the y-axis, what is its image point?

• (2,7)

• (2,-7)

• (-2,-7)

• (7,-2)

Multiple Choice

If a point remains unchanged after a reflection, then it lies on...

• the line of symmetry

• itself

• the origin

• point (5,6)