Warm Up

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Warm Up - PowerPoint PPT Presentation

Warm Up. Tell whether the ratios form a proportion. Find the missing number. Translations. I can : Define and identify translations. Understand prime notation to describe an image after a translation.

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Presentation Transcript
Warm Up

Tell whether the ratios form a proportion.

Find the missing number.

Translations

I can:

• Define and identify translations.
• Understand prime notation to describe an image after a translation.
• I can describe the changes occurring to the x and y coordinates of a figure after a translation.

Vocabulary:

• Transformations
• Translations
• Congruent Figures
• Parallel lines
Transformations

change the position of a shape on a coordinate plane.

*What that really means is that a shape is moving from one place to another.

Translation (Slide)

The action of sliding a figure in any direction.

*We use an arrow to represent the direction of the slide.

A translation does not need to be in a vertical or horizontal direction.

• It can also be in a diagonal direction.
Translation on Lines
• The size stays the same, the object is just slid to a new location.
• The lines are considered parallel lines- lines are parallel if they lie in the same plane, and are the same distance apart over their entire length.
Translation on Angles
• The angle degree stays the same, the angle is just slid to a new location.
Congruent Figures

Figures with the same size and shape.

Prime Notation

Way to label an image after a transformation.

Example:

A B A’ B’

(original before transformation)(image after transformation)

A’ is read as “A prime.”

Coordinate Plane

A translation across the y-axis

Coordinate Plane

A translation across the x-axis

Warm Up

Tell whether the shaded figure is a translation of the non-shaded figure. If it is a translation, use an arrow to represent the direction of the slide.

1. 2.

3. 4.

Reflections

I can:

• Define and identify reflections.
• Understand prime notation to describe an image after reflection.
• Identify lines of reflection.
• I can describe the changes occurring to the x and y coordinates of a figure after a reflection.

Vocabulary:

• Reflections
• Line of Reflection
• Line of Symmetry
Reflection (Flip)

A transformation representing a flip of a figure over a point, line, or plane.

A reflection creates a mirror image of the original figure.

• The original figure and its image are congruent.
Line of Reflection

A line in which you reflect a figure over.

Line of Symmetry

A line that can be drawn through a plane figure so that the figure on one side is the reflection image of the figure on the opposite side.

Reflection of Lines
• The size stays the same, the object is just the mirror image of itself.
Reflection of Angles
• The angle degree stays the same, the angle is just the mirror image of the original angle.

Horizontal flip:

• Vertical flip:

Reflection

Click on this trapezoid to see reflection.

The result of a figure flipped over a line.

Coordinate Plane

A reflection across the y-axis

RULE: (x, y)  (-x, y)

Coordinate Plane

A reflection across the x-axis

RULE: (x, y)  (x, -y)

Warm Up

Tell whether the shaded figure is a reflection of the non-shaded figure.

1. 2.

3. 4.

Lesson 3-3: Rotations

I can:

• Define and identify rotations.
• Identify corresponding sides.
• Understand prime notation to describe an image after a rotation.
• Identify center of rotation.
• Identify direction and degrees of a rotation.

Vocabulary:

• Rotations
• Angle of Rotation
• Center of Rotation
Rotations (Turns)

A transformation in which a figure is rotated about a point called the center of rotation.

Angle of Rotation

The number of degrees a figure rotates.

90 Degree Turn

Center of Rotation

The point in which a figure is rotated.

Click the

triangle to

see rotation

Turning a figure around a point or a vertex

Rotation

Clockwise Rotations
• 90 Degree Rotation:
• 180 Degree Rotation:
Counter-Clockwise Rotations
• 90 Degree Rotation:
• 180 Degree Rotation:
Rotations of Lines
• A line that rotates remains the same length, but will not necessarily remain parallel.

Same length; rotated 90 degrees clockwiseLines are not parallel

Rotations of Angles
• Angles that are rotated will remain the same degree measure.

Same degree measure; rotated 90 degrees counter-clockwise

Rotation

180 Degree Clockwise Rotation

Lesson 3-4: Dilations

I can:

• I can define dilations as a reduction or enlargement of a figure.
• I can identify the scale factor of the dilation.

Vocabulary:

• Dilations
• Center of Dilation
• Similar
• Scale Factor
• Enlargement
• Reduction
Dilations(Shrink or Enlargement)

A transformation in which a figure is made larger or smaller with respect to a fixed point called the center of dilation.

Center of Dilation

In a dilation, it is a fixed point that a figure is enlarged or reduced with respect to it.

Similar

The original figure and its image have the same shape but a different size.

Scale Factor

The ratio of the side lengths of the image to the corresponding side lengths of the original figure.

To dilate a figure in the coordinate plane, multiply the coordinates of each vertex by a scale factor.

• We will represent the scale factor with the variable k.
Enlargement

When k>1

Examples:

• Scale factor = 3
• Scale factor = 8
• Scale factor = 11
Reduction

When 0<k<1

Examples:

• Scale factor = 1/3
• Scale factor = 5/6
• Scale factor = 9/10
Scale Factor and Center of Dilation

Here we have Igor. He is 3 feet tall and the greatest width across his body is 2 feet.

He wishes he were 6 feet tall with a width of 4 feet.

His center of dilation would be where the length and greatest width of his body intersect.

He wishes he were larger by a scale factor of 2.

Are the following enlarged or reduced??

C

A

Scale factor of 1.5

D

Scale factor of 3

B

Scale factor of 0.75

Scale factor of 1/5