SOL Objective(s):
7.8 The student, given a polygon in the coordinate plane, will represent transformations (reflections, dilations, rotations, and translations) by
graphing in the coordinate plane.
8.8 The student will
a) apply transformations to plane figures; and
b) identify applications of transformations.
graphing in the coordinate plane.
8.8 The student will
a) apply transformations to plane figures; and
b) identify applications of transformations.
Khan Phrases:Translations of Polygons
Reflecting Points Rotation of Polygons 
The Basics and Background Information
• A rotation of a geometric figure is a turn of the figure around a fixed point. The point may or may not be on the figure. The fixed point is called the center of
rotation.
• A translation of a geometric figure is a slide of the figure in which all the points on the figure move the same distance in the same direction.
• A reflection is a transformation that reflects a figure across a line in the plane.
• A dilation of a geometric figure is a transformation that changes the size of a figure by scale factor to create a similar figure.
• 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 A′ (read as “ prime”.)
8th grade
• A rotation of a geometric figure is a clockwise or counterclockwise turn of the figure around a fixed point. The point may or may not be on the figure. The fixed point is called the center of rotation.
• A reflection of a geometric figure moves all of the points of the figure across an axis. Each point on the reflected figure is the same distance from the axis as
the corresponding point in the original figure.
• A translation of a geometric figure moves all the points on the figure the same distance in the same direction.
• A dilation of a geometric figure is a transformation that changes the size of a figure by a scale factor to create a similar figure.
• Practical applications may include, but are not limited to, the following:
– A rotation of the hour hand of a clock from 2:00 to 3:00 shows a turn of 30° clockwise;
– 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.
• The image of a polygon is the resulting polygon after a transformation. The preimage is the original polygon before the transformation.
• A transformation of preimage point A can be denoted as the image A′ (read as “ prime”.)
rotation.
• A translation of a geometric figure is a slide of the figure in which all the points on the figure move the same distance in the same direction.
• A reflection is a transformation that reflects a figure across a line in the plane.
• A dilation of a geometric figure is a transformation that changes the size of a figure by scale factor to create a similar figure.
• 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 A′ (read as “ prime”.)
8th grade
• A rotation of a geometric figure is a clockwise or counterclockwise turn of the figure around a fixed point. The point may or may not be on the figure. The fixed point is called the center of rotation.
• A reflection of a geometric figure moves all of the points of the figure across an axis. Each point on the reflected figure is the same distance from the axis as
the corresponding point in the original figure.
• A translation of a geometric figure moves all the points on the figure the same distance in the same direction.
• A dilation of a geometric figure is a transformation that changes the size of a figure by a scale factor to create a similar figure.
• Practical applications may include, but are not limited to, the following:
– A rotation of the hour hand of a clock from 2:00 to 3:00 shows a turn of 30° clockwise;
– 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.
• The image of a polygon is the resulting polygon after a transformation. The preimage is the original polygon before the transformation.
• A transformation of preimage point A can be denoted as the image A′ (read as “ prime”.)
Essential Knowledge and Skills
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
• 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.
• Identify the coordinates of the image of a right triangle or rectangle that has been rotated 90° or 180° about the origin.
• Identify the coordinates of the image of a right triangle or a rectangle that has been reflected over the x or yaxis.
• Identify the coordinates of a right triangle or rectangle that has been dilated. The center of the dilation will be the origin.
• Sketch the image of a right triangle or rectangle translated vertically or horizontally.
• Sketch the image of a right triangle or rectangle that has been rotated 90° or 180° about the origin.
• Sketch the image of a right triangle or rectangle that has been reflected over the x or yaxis.
• Sketch the image of a dilation of a right triangle or rectangle limited to a scale factor of 1/4, 1/2, 2, 3 or 4.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to...
• Demonstrate the reflection of a polygon over the vertical or horizontal axis on a coordinate grid.
• Demonstrate 90°, 180°, 270°, and 360°clockwise and counterclockwise rotations of a figure on a coordinate grid. The center of rotation will be limited to the origin.
• Demonstrate the translation of a polygon on a coordinate grid.
• Demonstrate the dilation of a polygon from a fixed point on a coordinate grid.
• Identify practical applications of transformations including, but not limited to, tiling, fabric, and wallpaper designs, art and scale drawings.
• Identify the type of transformation in a given example.
• 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.
• Identify the coordinates of the image of a right triangle or rectangle that has been rotated 90° or 180° about the origin.
• Identify the coordinates of the image of a right triangle or a rectangle that has been reflected over the x or yaxis.
• Identify the coordinates of a right triangle or rectangle that has been dilated. The center of the dilation will be the origin.
• Sketch the image of a right triangle or rectangle translated vertically or horizontally.
• Sketch the image of a right triangle or rectangle that has been rotated 90° or 180° about the origin.
• Sketch the image of a right triangle or rectangle that has been reflected over the x or yaxis.
• Sketch the image of a dilation of a right triangle or rectangle limited to a scale factor of 1/4, 1/2, 2, 3 or 4.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to...
• Demonstrate the reflection of a polygon over the vertical or horizontal axis on a coordinate grid.
• Demonstrate 90°, 180°, 270°, and 360°clockwise and counterclockwise rotations of a figure on a coordinate grid. The center of rotation will be limited to the origin.
• Demonstrate the translation of a polygon on a coordinate grid.
• Demonstrate the dilation of a polygon from a fixed point on a coordinate grid.
• Identify practical applications of transformations including, but not limited to, tiling, fabric, and wallpaper designs, art and scale drawings.
• Identify the type of transformation in a given example.
Vocabulary and Things to Know:Transformations
Translations: slides up/down and/or sideways Reflections: flipped image over a line of symmetry Roation: turned image around the center of rotation Dilation: reduced or enlarged image Line of symmetry Center of rotation Coordinate plane X and Y axes Quadrants Coordinates Scale Factor Name a new point with prime... 
Be Able To:Recognize and name original and new images of figures.
When given an original figure and rules, determine the cooredinates of a new image. When given the new image and the rules to make it, determine the original image. When given the original and new image, determine the rules and/or what kind of transformation made it. 
The topic: What is it and what will we learn?
Transformational GeometrySolid concepts demonstrated.


Reflection, Rotation, and Translation


Motion GeometryReal world applications of transformations are shown.


MathAids.com 
Kuta Software
