Lesson 9-7 Dilations Rigor: Dilate figures on and off a coordinate plane, calculate the scale factor of a dilation Relevance – Optometry, art, graphic.

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Lesson 9-7 Dilations Rigor: Dilate figures on and off a coordinate plane, calculate the scale factor of a dilation Relevance – Optometry, art, graphic design

What is a Dilation? k

Enlargements and Reductions  Enlargement: scale factor is greater than 1  Reduction: 0 < scale factor < 1  The center of dilation can be inside or outside the figure, on a vertex or on a side of the figure. The center of dilation determines the position of the image, the scale factor determines the size.

EX 1: What is the scale factor? Is the dilation a reduction or an enlargement?  The image is in blue, and the pre-image is in black. A)B)

EX 2: Graph the image after a dilation about the origin with the given scale factor. A) k = 2B) y = x + 4; k = 1/2

EX 3: An artist is creating a large painting from a photo by dividing the photo into squares and dilating each square by a scale factor of 4. If the photo is 20cm by 25cm, what is the perimeter of the painting?

Negative Scale Factors  If k is negative, the transformation is a composition of a dilation & a 180 o rotation about the center of dilation  EX 4: Draw the image of ΔABC with vertices A(-1,1), B( -3, -1), and C( -1, -2) under the dilation centered at the origin and k = - 2.

EX 5: Constructions!  Turn to page 405 in your core book  Example 1 and practice 1 – 3 together

9-7 Classwork from the textbook  Heading: 9-7 CW pg 653  Problems: #2 – 12 even, 17, 18, 28, Homework from the core book  Pg 407 #1 – 3 and pg 408 #1, 2, 4 – 6  Due Thursday for Periods 1, 3, 5  Due Friday for Periods 2, 4, 7