Reflection

Transformations (Math 8)

by Mrs. Moody

Dilations

December 4, 2020

​Reflection

• ​"flip"

• ​Shapes are usually reflected over the x-axis or the y-axis.

• ​The image is congruent with the pre-image (starting shape).

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

Warm-up: What does the scale factor do in a dilation?

• Tells you how much the image grows or shrinks

• Tells you what the center of dilation is

• There's not enough information here to answer this

• Nothing, it's unnecessary information

Multiple Choice

Find K' if the figure is reflected across the x-axis

• (4, 1))

• (-1, -4)

• (1, -4)

• (1, 4)

Scale Factors

What do they really do?

Multiple Choice

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

• y-axis

• x-axis

Scale Factors are just as they sound

• Factors (multipliers) that scale (change the size of) a shape

• Scale factors can do one of two things: grow or shrink an object

• A scale factor larger than one (>1) makes an object get larger --> could be a fraction or a whole number

• A scale factors smaller than one (<1) makes an object get smaller

​Translation

• ​"slide"

• ​After the translation, the shape is congruent.

• ​Example of the translation equation is

Multiple Select

Which scale factors would increase an image?

• $$\frac{3}{2}$$

• $$\frac{1}{2}$$

• $$3.5$$

• $$\frac{2}{1}$$

• 5
  

Multiple Choice

What transformation is happening? (x, y) ----> (x + 2, y - 3) 

• slide up 2, left 3

• slide right 2, up 3

• slide right 2, down 3

• slide left 3, right 2

Multiple Select

Which scale factors shrink an image?

• $$0.5$$

• $$\frac{3}{4}$$

• $$1$$

• $$\frac{2}{1}$$

• $$\frac{3}{2}$$

Multiple Choice

What is the algebraic notation of a figure is Translated 6 units right and 5 units up?

• (x, y) --> (x - 6, y + 5)

• (x, y) --> (x + 6, y + 5)

• (x, y) --> (x + 5, y - 6)

• (x, y) --> (6x, 5y)

Multiple Select

What are the properties of dilations?

• Changes the size of an object

• Changes the shape of an object

• Changes one side but not the others

• Changes all the sides equally

• Changes angle measures

Multiple Choice

The dashed figure is the image of the solid figure.  What is the Algebraic Notation for the Translation?

• (x, y) --> (x - 7, y + 4)

• (x, y) --> (x + 7, y - 4)

• (x, y) --> (x + 4, y - 7)

• (x, y) --> (7x, 4y)

What happens if you aren't given the scale factor?

• Set up a proportion

• Solve for the missing side

​Rotations

• ​"turn"

• ​Clockwise and Counter Clockwise

• ​90 degrees, 180 degrees, 270 degrees

• ​images are congruent

But...what's a proportion?

A proportion is a ratio (fraction) that compares the corresponding pairs of sides

Multiple Choice

Does the image show a rotation? If so, what is the angle of rotation?

• 90° counterclockwise

• 180° counterclockwise

• 270° counterclockwise

• Not a rotation

Proportion Example

Multiple Choice

The image A'B'C' is a rotation of ABC.

• True

• False

How do we solve a proportion now?

Multiple Choice

What type of rotation does this represent (from red to blue)?

• 270⁰ clockwise

• 360⁰

• 90⁰ counterclockwise

• 180⁰

There is a proportions practice sheet in Google Classroom

Please go work on that

Email me if you have any questions :)

Multiple Choice

The red triangle represents what type of rotation:

• 180° Clockwise

• 90° Counter Clockwise

• 90° Clockwise

• 270° Counter Clockwise