 # Coordinate Transformations - Rotation, Reflection, Translation, Dilations

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Examples, solutions, worksheets, videos, and lessons to help Grade 8 students learn how to describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Common Core: 8.G.3

### Suggested Learning Targets

• I can define dilations as a reduction or enlargement of a figure.
• I can identify scale factor of the dilation.
• I can describe the effects of dilations, translations, rotations, and reflections on 2-D figures using coordinates.

### Transformation Rules on the Coordinate Plane

Translation: Each point moves a units in the x-direction and b units in the y-direction.
(x, y) → (x + a, y + b)

Reflection across the x-axis: Each x-value stays the same and each y-value becomes opposite of what it was. (x, y) → (x, −y)

Reflection across the y-axis: Each y-value stays the same and each y-value becomes opposite of what it was. (x, y) → (−x, y)

Reflection across the line y=x: The x and y values switch places. (x, y) → (y, x)

Rotation 90° about the origin: Each y-value becomes opposite of what it was. The x and y values switch places.
(x, y) → (−y, x)

: Each x and y value becomes opposite of what it was.
(x, y) → (−x, −y)

Rotation 270° about the origin: Each x value becomes opposite of what it was. The x and y values switch places.
(x, y) → (y, −x)

Dilation with respect to the origin and scale factor of k: (x, y) → (kx, ky)

Coordinate Transformation and Dilation

Transformational Geometry- Dilations
In this tutorial you will learn about dilations and scale factors.

Transformations on the coordinate plane
Rotation, Reflection, Translation, Dilations. Dilation of a tilted shape 8.G.3
Dilate a parallelogram by a scale factor between 0 and 1
In the coordinate plane below, a dilation about the origin is performed on Figure A, which results in Figure A'. What is the scale factor and how does it alter the area and perimeter? Dilations on the coordinate plane (with different values of scale factor, k) Geometric Transformations
Demonstrate geometric transformation using Geogebra
Rotation, Reflection, Translation, Dilations.

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