#### Math - 2018-19

# 8.7 - Transformations

8.7The student willa) given a polygon,

applytransformations, to include translations, reflections, and dilations, in the coordinate plane;b)

identifypractical applications of transformations.

*Adopted: 2016*

### BIG IDEAS

- I can design a wallpaper pattern, tile a floor, create a
quilt, and piece together a stain glass window.

- I will
understand that an ordered pair represents a unique location in space and be
able to find specific locations on a grid and see how moving an object does not
change its size or shape.

### UNDERSTANDING THE STANDARD

· Translations and reflections maintain congruence between the preimage and image but change location. Dilations by a scale factor other than 1 produce an image that is not congruent to the preimage but is similar. Reflections change the orientation of the image.

· A transformation of a figure, called preimage, changes the size, shape, and/or position of the figure to a new figure, called the image.

·
A
transformation of preimage point *A *can
be denoted as the image *A’ *(read as “*A* prime”).

· A reflection is a transformation in which an image is formed by reflecting the preimage over a line called the line of reflection. Each point on the image is the same distance from the line of reflection as the corresponding point in the preimage.

· A translation is a transformation in which an image is formed by moving every point on the preimage the same distance in the same direction.

·
A dilation
is a transformation in which an image is formed by enlarging or reducing the
preimage proportionally by a scale factor from the center of dilation (limited
to the origin in grade eight).

A dilation of a figure and the original figure are similar. The center of dilation may or may not be on
the preimage.

·
The result
of first translating and then reflecting over the *x*- or *y*-axis may not
result in the same transformation of reflecting over the *x*- or *y*-axis and then
translating.

· Practical applications may include, but are not limited to, the following:

- A reflection of a boat in water shows an image of the boat flipped upside down with the water line being the line of reflection;

- A translation of a figure on a wallpaper pattern shows the same figure slid the same distance in the same direction; and

- A dilation of a model airplane is the production model of the airplane.

### ESSENTIALS

- How does the
transformation of a figure on the coordinate grid affect the congruency,
orientation, location and symmetry of an image?

Translations, rotations and reflections maintain congruence between the preimage and image but change location. Dilations by a scale factor other than 1 produce an image that is not congruent to the pre-image but is similar. Rotations and reflections change the orientation of the image.

**The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and representations to**

·
8.7a_{1}** **Given
a preimage in the coordinate plane, **identify**
the coordinate of the image of a polygon that has been translated vertically,
horizontally, or a combination of both.

·
8.7a_{5}** Sketch**
the image of a polygon that has been translated vertically, horizontally, or a
combination of both.

·
8.7a_{2}** **Given
a preimage in the coordinate plane, **identify**
the coordinates of the image of a polygon that has been reflected over the *x*- or *y*-axis.

·
8.7a_{6}** Sketch**
the image of a polygon that has been reflected over the *x*- or *y*-axis.

·
8.7a_{4}** **Given
a preimage in the coordinate plane, **identify**
the coordinates of the image of a polygon that has been translated and
reflected over the *x*-or *y*-axis, or reflected over the *x*- or *y*-axis and then translated.

·
8.7a_{3}** **Given
a preimage in the coordinate plane, **identify**
the coordinates of the image of a right triangle or a rectangle that has been
dilated. Scale factors are limited to , , 2, 3, or 4. The center of the dilation will be the
origin.

·
8.7a_{7}** Sketch**
the image of a dilation of a right triangle or a rectangle limited to a scale
factor of , ,
2, 3, or 4. The center of the dilation will be the origin.

### KEY VOCABULARY

translation, reflection, rotation, polygon, vertical axis, horizontal
axis, coordinate grid, clockwise, counterclockwise, origin, tiling,
fabric/wallpaper design, scale drawing

*Updated: Nov 20, 2018*