What is a translation?

A translation is a horizontal or vertical shift of a point or figure. The image produced by translation is congruent to the original.

What is a reflection?

A reflection is a mirror image of a point or figure taken across a reflection line. The reflections are usually across the x- or y-axis of a coordinate plane.

Are all reflected images congruent to the original?

Yes; reflecting a figure does not change its angles or side lengths, so the image is congruent to the preimage.

How do you know where to place a point on a coordinate plane?

Points are defined using an ordered pair (x, y) so that the first number is the distance from the origin on the x-axis, and the second is the distance from the origin on the y-axis.

Can you perform more than one kind of transformation on a figure to get the image?

Yes, I can perform multiple transformations to get an image. The order that I perform the transformations in matters, so I need to follow the order of transformations. This is similar to the order of operations. The order is rotations, reflections, dilations, and then translations.

What is a scale factor?

A scale factor is the value I multiply the coordinates of the original point by to get its image point in a dilation.

What is the difference between an enlargement and a reduction?

Enlargements and reductions are both dilations, but an enlargement produces an image that is larger (farther from the origin) than the original, and a reduction produces an image that is smaller (closer to the origin). Enlargements have scale factors larger than 1, and reductions have scale factors between 0 and 1.

How do you rotate a figure 90°?

First, I need to know whether to rotate clockwise or counterclockwise. The mapping rule for a clockwise 90° rotation is (x,y)→(y,-x). If I want to rotate counterclockwise, I need to find the equivalent angle: 270° clockwise is the same as 90° counterclockwise. The mapping rule for a clockwise 270° rotation is (x,y)→(-y,x).

How can you determine what transformation was used to create an image?

First, find the corresponding vertex points. Then determine if the image is in the same orientation or a different one. If the orientation is different, look for a rotation or reflection. If the orientation is the same, check if both figures are the same size. If they are not the same size, then a dilation was used. Divide the image coordinates by the corresponding original coordinates. The answer gives the scale factor for the dilation. If there was no dilation, then the difference between the image coordinates and the original coordinates gives the translation.

What does it mean for two 2D figures to be similar?

Two 2D figures are similar if all the corresponding angles are equal, and all side lengths share the same scale factor between them. Translations, reflections, dilations, and rotations all create similar shapes.

Transformations: Rotations & Dilations

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What you will learn from this videoWhat you will learn

We’ll learn that dilations make shapes larger and smaller.
We will also learn that rotations turn shapes around a point on a coordinate plane.
And we'll see how this knowledge can help us make art, edit photos, and even solve a mystery!

Discussion Questions
- Before Video
  What is a translation?ANSWER
  - A translation is a horizontal or vertical shift of a point or figure. The image produced by translation is congruent to the original.
  What is a reflection?ANSWER
  - A reflection is a mirror image of a point or figure taken across a reflection line. The reflections are usually across the x- or y-axis of a coordinate plane.
  Are all reflected images congruent to the original?ANSWER
  - Yes; reflecting a figure does not change its angles or side lengths, so the image is congruent to the preimage.
  How do you know where to place a point on a coordinate plane?ANSWER
  - Points are defined using an ordered pair (x, y) so that the first number is the distance from the origin on the x-axis, and the second is the distance from the origin on the y-axis.
  Can you perform more than one kind of transformation on a figure to get the image?ANSWER
  - Yes, I can perform multiple transformations to get an image. The order that I perform the transformations in matters, so I need to follow the order of transformations. This is similar to the order of operations. The order is rotations, reflections, dilations, and then translations.
- After Video
  What is a scale factor?ANSWER
  - A scale factor is the value I multiply the coordinates of the original point by to get its image point in a dilation.
  What is the difference between an enlargement and a reduction?ANSWER
  - Enlargements and reductions are both dilations, but an enlargement produces an image that is larger (farther from the origin) than the original, and a reduction produces an image that is smaller (closer to the origin). Enlargements have scale factors larger than 1, and reductions have scale factors between 0 and 1.
  How do you rotate a figure 90°?ANSWER
  - First, I need to know whether to rotate clockwise or counterclockwise. The mapping rule for a clockwise 90° rotation is (x,y)→(y,-x). If I want to rotate counterclockwise, I need to find the equivalent angle: 270° clockwise is the same as 90° counterclockwise. The mapping rule for a clockwise 270° rotation is (x,y)→(-y,x).
  How can you determine what transformation was used to create an image?ANSWER
  - First, find the corresponding vertex points. Then determine if the image is in the same orientation or a different one. If the orientation is different, look for a rotation or reflection. If the orientation is the same, check if both figures are the same size. If they are not the same size, then a dilation was used. Divide the image coordinates by the corresponding original coordinates. The answer gives the scale factor for the dilation. If there was no dilation, then the difference between the image coordinates and the original coordinates gives the translation.
  What does it mean for two 2D figures to be similar?ANSWER
  - Two 2D figures are similar if all the corresponding angles are equal, and all side lengths share the same scale factor between them. Translations, reflections, dilations, and rotations all create similar shapes.
Vocabulary
- Coordinate plane DEFINE
- x-axis DEFINE
- y-axis DEFINE
- Origin DEFINE
- Point DEFINE
- Transformation DEFINE
- Image DEFINE
- Dilation DEFINE
- Translation DEFINE
- Reflection DEFINE
- Scale Factor DEFINE
- Rotation DEFINE
Reading Material
Practice Word Problems
Practice Number Problems
Lesson Plan
Teacher Guide
Assessment
Online Quiz Game Quiz PDF Exit Ticket