1. 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.

2. 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.

3. 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)

4. Translation: a figure is slid in any direction.
(x, y) (x + a, y + b)

5. Dilation: a figure is enlarged or reduced.
(x, y) (kx, ky)

6. Rotation: a figure is turned around a point.
(x, y) (-y, x)
180° rotation:
(x, y) (-x, -y)

7. Ex. 1: Identify each transformation as a reflection, translation, dilation, or rotation.b)
Translation c)
Rotation

8. d)
Reflection

9. 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’

10. 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.

11. 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.

12. 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