DilationsDilations

VocabularyVocabulary Dilation: The image created by Dilation: The image created by

enlarging or reducing a figure.enlarging or reducing a figure. Center: The center of a dilation is a Center: The center of a dilation is a

fixed point used for measurement when fixed point used for measurement when altering the size of the figure.altering the size of the figure.

Enlargement: An image that is larger Enlargement: An image that is larger than the original figure. An enlargement than the original figure. An enlargement has a scale factor greater than 1.has a scale factor greater than 1.

Reduction: An image that is smaller Reduction: An image that is smaller than the original figure. A reduction has than the original figure. A reduction has a scale factor between 0 and 1a scale factor between 0 and 1

A dilation is ALWAYS similar to the A dilation is ALWAYS similar to the original figure. So the corresponding original figure. So the corresponding angles are congruent and angles are congruent and corresponding sides are proportional.corresponding sides are proportional.

Scale Factor: The ratio of a length on Scale Factor: The ratio of a length on the image to a length on the original the image to a length on the original figure is the scale factor of the figure is the scale factor of the dilation.dilation.

ExamplesExamplesGraph Graph JKL with vertices

J (3,8), K (10,6), and L (8,2). Then graph its image J’K’L’ after a dilation with a scale factor of ½.

Find the coordinates of the image of Find the coordinates of the image of triangle JKL after a dilation with each triangle JKL after a dilation with each scale factor. Then graph JKL and J’K’L’.scale factor. Then graph JKL and J’K’L’.

A) Scale Factor 3A) Scale Factor 3 B) Scale Factor 1/3B) Scale Factor 1/3

Find and Classify a Scale Find and Classify a Scale FactorFactor

Quadrilateral V’Z’X’W’ is a dilation of Quadrilateral V’Z’X’W’ is a dilation of quadrilateral VZXW. Find the scale quadrilateral VZXW. Find the scale factor of the dilation, and classify it as factor of the dilation, and classify it as an enlargement or a reduction.an enlargement or a reduction.

Graph V’Z’X’W’Graph V’Z’X’W’ Graph VZXWGraph VZXW

V’ (-5, 5)V’ (-5, 5) V (-2,2)V (-2,2)

Z’ (-2.5, 7.5)Z’ (-2.5, 7.5) Z (-1, 3)Z (-1, 3)

X’ (2.5, 6)X’ (2.5, 6) X (1, 2.5)X (1, 2.5)

W’ (5, 2.5)W’ (5, 2.5) W (2, 1)W (2, 1)

Write a ratio of the x-or the y-Write a ratio of the x-or the y-coordinate of one vertex of the coordinate of one vertex of the DILATION to the x- or y-coordinate of DILATION to the x- or y-coordinate of the CORRESPONDING vertex of the the CORRESPONDING vertex of the original figure.original figure.

Let’s use V and V’ since we have whole Let’s use V and V’ since we have whole numbers.numbers.

V (-2, 2)V (-2, 2) V’ (-5, 5)V’ (-5, 5)

Y-coordinate of V’Y-coordinate of V’ = = 55Y-coordinate of V 2Y-coordinate of V 2

Our scale factor is 5/2Our scale factor is 5/2

Based on our scale factor our image is Based on our scale factor our image is an enlargement since 5/2 is greater an enlargement since 5/2 is greater than 1.than 1.

Remember 5/2 is an improper fraction Remember 5/2 is an improper fraction so if we change this into a mixed so if we change this into a mixed number we get 2.5number we get 2.5

Carleta’s optometrist dilates her pupils Carleta’s optometrist dilates her pupils by a factor of 5/3. if her pupil before by a factor of 5/3. if her pupil before dilation has a diameter of 5 milimeters, dilation has a diameter of 5 milimeters, find the new diameter after her pupil is find the new diameter after her pupil is dilateddilated