# 7.7 - Transformations

7.7  The student will apply translations and reflections of right triangles or rectangles in the coordinate plane.

### 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

2016 VDOE Curriculum Framework - 7.7 Understanding

·  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 (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

·  7.71  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.

·  7.72  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.

·  7.73  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.

·  7.74  Sketch the image of a right triangle or rectangle that has been translated vertically, horizontally, or a combination of both.

·  7.75  Sketch the image of a right triangle or rectangle that has been reflected over the x- or y-axis.

·  7.76  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: Nov 20, 2018