#### Math - 2019-20

# 7.7 - Transformations

7.7The student willapplytranslations and reflections of right triangles or rectangles in the coordinate plane.

*Adopted: 2016*

### BIG IDEAS

- I can find specific
locations on a grid and see how moving an object does
not change its size or shape.

- I will
understand that an ordered pair represents a unique location in space.

### UNDERSTANDING THE STANDARD

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

· Translations and reflections do not change the size or shape of a figure (e.g., the preimage and image are congruent figures). Translations and reflections change the position of a figure.

· 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 reflection is a transformation in which an image is formed by reflecting the preimage over a line called the line of reflection. All corresponding points in the image and preimage are equidistant from the line of reflection.

· The image of a polygon is the resulting polygon after the transformation. The preimage is the polygon before the transformation.

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

·
The preimage
of a figure that has been translated and then reflected over the *x*- or*
y*-axis may result in a different transformation than the preimage of a
figure that has been reflected over the *x*-
or *y*-axis and then translated.

### ESSENTIALS

- How does the
transformation of a figure affect the size, shape and position of that figure?

Translations, rotations and reflections do not change the size or shape of a figure. A dilation of a figure and the original figure are similar. Reflections, translations and rotations usually change the position of the figure.

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

·
7.7_{1} Given a preimage in the coordinate plane, **identify** the coordinates of the image
of a right triangle or rectangle that has been translated either vertically,
horizontally, or a combination of a vertical and horizontal translation.

·
7.7_{2} Given a preimage in the coordinate plane, **identify** the coordinates of the image
of a right triangle or a rectangle that has been reflected over the *x*- or *y*-axis.

·
7.7_{3} Given a preimage in the coordinate plane, **identify** the coordinates of the image
of a right triangle or rectangle that has been translated and reflected over
the *x*- or *y*-axis or reflected over the *x*-
or *y*-axis and then translated.

·
7.7_{4} **Sketch**
the image of a right triangle or rectangle that has been translated vertically,
horizontally, or a combination of both.

·
7.7_{5} **Sketch**
the image of a right triangle or rectangle that has been reflected over the *x*- or *y*-axis.

·
7.7_{6} **Sketch**
the image of a right triangle or rectangle that has been translated and
reflected over the *x*- or *y*-axis or reflected over the *x*- or *y*-axis and then translated.

### KEY VOCABULARY

coordinate plane, transformations, reflection, dilation, rotation,
translation, scale factor, center of rotation, vertical, horizontal, x-axis,
y-axis, right triangle, prime, sketch, coordinates, 180 degrees, 90 degrees

*Updated: Jul 30, 2019*