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**Lesson 4.2- Transformations on the Coordinate Plane, pg. 197**

Objectives: To transform figures by using reflections, translations, dilations, and rotations. To transform figures on a coordinate plane by using reflections, translations, dilations, and rotations.

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**Vocabulary Transformations: movements of geometric figures.**

Pre-image: the position of the figure before the transformation. Image: the position of the figure after the transformation.

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**Transformations on the Coordinate Plane**

Reflection- the figure is flipped over a line. Reflection over the x-axis: (x, y) (x, -y) Reflection over the y-axis: (x, y) (-x, y)

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**Translation: a figure is slid in any direction.**

(x, y) (x + a, y + b)

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**Dilation: a figure is enlarged or reduced.**

(x, y) (kx, ky)

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**Rotation: a figure is turned around a point.**

(x, y) (-y, x) 180° rotation: (x, y) (-x, -y)

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**Ex. 1: Identify each transformation as a reflection, translation, dilation, or rotation.**

b) Translation c) Rotation

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d) Reflection

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**Ex. 2: A trapezoid has vertices W(-1, 4) X(4, 4), Y(4, 1), and Z(-3, 1)**

A trapezoid is reflected over the y-axis. Find the coordinates of the image. Graph the trapezoid WXYZ and its image W’X’Y’Z’

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**Ex. 3: Triangle ABC has vertices A(-2,1), B(2, 4) and C(1,1)**

Find the coordinates of the vertices of the image if it is translated 3 units to the right and 5 units down. Graph the triangle ABC and its image.

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**Ex. 4: A trapezoid has vertices E(-1, 2), F(2, 1), G(2, -1), and H(-1, -2)**

Find the coordinates of the dilated trapezoid E’F’G’H’ if the scale factor is 2. Graph the pre-image and its image.

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**SUMMARY Reflection- the figure is flipped over a line.**

Translation: a figure is slid in any direction. Dilation: a figure is enlarged or reduced Rotation: a figure is turned around a point. Skills Practice Workbook, Lesson 4.2

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