Dilations.

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Graph dilations on a coordinate plane.

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Presentation transcript:

Dilations

What’s the difference?? Undilated Dilated

Vocabulary Dilation: a transformation that changes the size of a figure but NOT its shape. Similar: Two figures are similar if they have the same shape but not necessarily the same size. Scale Factor: Describes how much the figure is enlarged or reduced. Represented by the letter K You can find the image of a point by multiplying each coordinate by k.

To find the coordinates of the new image after a dilation: 1. Multiply each x and y-coordinate in each of the ordered pairs by the given scale factor K. 2. Then connect the vertices of the new ordered pairs.

Vocabulary Enlargement: When the image is larger than the original. Multiply by a scale factor K greater than 1, K>1.

Vocabulary Reduction: When the image is smaller than the original. Multiply by a scale factor K greater than 0 and smaller Than1, 0<K<1

Draw the image of the figure after a dilation by a scale factor of 3. Step 1: Label the ordered pair of each vertex. (1,3) (2,2) (2,1) (1, 1)

A(1,1)  (1●3, 1●3)  A’(3,3) B(2,1)  (2●3, 1●3)  B’(6,3) Step 2: Multiply each coordinate in the ordered pairs by the scale factor 3. A(1,1)  (1●3, 1●3)  A’(3,3) B(2,1)  (2●3, 1●3)  B’(6,3) C(2,2)  (2●3, 2●3)  C’(6,6) D(1,3)  (1●3, 3●3)  D’(3,9)

Plot the new points. Connect the dots to form the dilated shape. Step 3: Plot the new points. Connect the dots to form the dilated shape. D’(3,9) C’(6,6) B’(6,3) A’(3, 3)

FIND AND CLASSIFY A SCALE FACTOR In the figure, segment X'Y' is a dilation of segment XY. Find the scale factor of the dilation and classify it as an enlargement or a reduction. Write a ratio using the x or y-coordinate of any vertex of the dilation to the x- or y-coordinate of the corresponding vertex of the original figure.

Find and Classify a Scale Factor (-4, 2) 1 2 (-2, 1) Answer: The scale factor is . Since < 1, the dilation is a reduction.

STOP HERE We will cover the following information during the next class.

Horizontal stretch Dilate the given figure according to the rule: (x, y) (2x, y) Multiply X coordinates by K=2 A (-1, 2) A’ (-2, 2) B (3, 2) B’ (6, 2) C (3, -1) C’(6, -1) D (-1, -1) D’ (-2, -1) 2. Graph A’ B’ C’ D’ A B D C

VERTICal stretch Dilate the given figure according to the rule: (x, y) (x, 5y) Multiply Y coordinates by K=5 A (-1, 1) A’ (-1, 5) B (1, 1) B’ (1, 5) C (1, -1) C’ (1, -5) D (-1, -1) D’ (-1, -5) 2. Graph A’ B’ C’ D’ A B D C

Horizontal shrink A A’ B’ C’ D’ B D C

vertical shrink A B A’ B’ C’ D’ D C