Presentation on theme: "11-19 S 6.7: Perform Similarity Transformations. Review: Transformations: when a geometric figure is moved or changed in some way to produce a new figure."— Presentation transcript:
Review: Transformations: when a geometric figure is moved or changed in some way to produce a new figure Image is what the new figure is called.
Congruence Transformations change the position of a figure without changing its size or shape. Three Types of the above: Translation Translation Reflection Reflection Rotation Rotation
Translation: every point on the figure is moved the same direction and distance (think of it as “ sliding ” )
Coordinate Notation for a translation: (x,y) (x+a, y+b) Ex. (x,y) (x + 5, y + 7) Each point (x,y) of the blue figure is translated horizontally a units and vertically b units Ex. (-5, -6) (0, 1) (same for other 2 vertices) a b x y Same orientation, just different position
Reflection: a line of reflection is used to create a mirror image of the original figure (think of it as “ flipping ” )
Multiply the y coordinate by -1 (x,y) (x,-y) Ex: (2, 5) (2, -5) Multiply the x coordinate by -1 (x,y) (-x,y) Ex: (1, 6) (-1, 6) Reflection in the x-axis Reflection in the x-axis Reflection in the y-axis Reflection in the y-axis y x y x (x,y) (x,-y) (-x,y) (x,y) Coordinate Notation for a Reflection
Rotation: a figure is turned about a fixed point called the center of rotation (think of it as “ turning in a circle ” )
90 clockwise Rotation 90 clockwise Rotation 60 counterclockwise rotation 60 counterclockwise rotation y y xx Rotation: need direction of rotation and degrees
Vocabulary: Dilation: a transformation that stretches (enlarges) or shrinks (reduces) a figure to create a similar figure If enlarged, called an enlargement. If reduced, called a reduction.
Center of Dilation: The fixed point from which the figure is enlarged or reduced (called “ with respect to... ” ; usually the origin)
Scale Factor of a Dilation: Ratio of the side length of the image to the corresponding side length of the original figure
Coordinate Notation for a Dilation With respect to the origin, (x, y) (kx, ky) where k is the scale factor Reduction: k is 0. Enlargement: k > 1
How to Draw a Dilation (Steps)-p.408 1. Plot the vertices given and connect with straight lines to create a geometric figure. 2. Draw rays from the origin through the vertices given that extend well beyond the vertices. 3. Open your compass the distance from the origin to one vertex.
4. Keeping the compass open that same distance, mark an arc on the ray that starts at the vertex. 5. The intersection of the ray and the arc mark is a vertex on the image. 6. Do the same for the other vertices and their rays.
S 6.7, Ex. 1-2, GP 1-2.ppt S 6.7, Ex. 1-2, GP 1-2.ppt (If absent, insert examples 1 & 2 from your textbook, on graph paper, in your notes, with solution shown)
Finding the scale factor and proving a figure is a dilation. The change from each vertex of the original figure to its corresponding vertex of the image must be by the same scale factor. S 6.7 Ex 3-4, GP 3-4.ppt S 6.7 Ex 3-4, GP 3-4.ppt (If absent, put examples 3 & 4 in your notes from the textbook. Use graph paper slips if appropriate.)