Dilations Dilations Dilations Dilations Dilations Dilations Dilations Section 9.5 Dilations Dilations Dilations Dilations Dilations

Determine the scale factor for a given dilation. Determine whether a dilation is an enlargement, a reduction, or a congruence transformation. Determine the scale factor for a given dilation. dilation similarity transformation Standard 11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids. Lesson 5 MI/Vocab

Dilation Center: C Scale Factor: r or k (the book uses both) Def: A transformation that maps every point P to a point P’ so that the following properties are true: P’ lies on The scale factor is:

Scale Factor If r > 1, the dilation is called an enlargement. If r < 1, the dilation is called a reduction. If r = 1, the dilation is called a congruence transformation. (Just like in chapter 7) A scale factor can also be found by comparing corresponding lengths in a ratio.

Example #1 r < 1 reduction Determine the scale factor, then state if the dilation is an enlargement, reduction or congruence transformation. r < 1 reduction

Example #2 r > 1 enlargement Determine the scale factor, then state if the dilation is an enlargement, reduction or congruence transformation. r > 1 enlargement

Theorem 9.2: If a dilation with center C and a scale factor of r transforms A to A’ and B to B’, then: A’B’ = |r|(AB) Algebraic hint: AB = Lesson 5 KC1

Example #3 Given PQ = 1, Q’R’ = 4, use the scale factor to find P’Q’ and QR. 1

Example #3 Given PQ = 1, Q’R’ = 4, use the scale factor to find P’Q’ and QR. 4

Determine Measures Under Dilations A. Find the measure of the dilation image C′D′ using the given scale factor for CD = 15, r = 3. Answer: 45 Lesson 5 Ex1

B. Find the measure of the preimage using the given scale factor if Determine Measures Under Dilations B. Find the measure of the preimage using the given scale factor if Multiply each side by Answer: 10.5 Lesson 5 Ex1

A. Find the measure of the dilation image A′B′ using the given scale factor for AB = 16, r = –2. Lesson 5 CYP1

B. Find the measure of the preimage using the given scale factor for A′B′ = 24, r = . Lesson 5 CYP1

Which diagram shows the dilation image of ΔLMN with center C and ? A. B. C. D. A B C D Lesson 5 CYP2

Multiply the coordinates by the scale factor. Theorem 9.3 If is the preimage of a dilation centered at the origin with a scale factor k, then the image is Multiply the coordinates by the scale factor. Lesson 5 TH2

COORDINATE GEOMETRY Trapezoid EFGH has vertices E(–8, 4), F(–4, 8), Dilations in the Coordinate Plane COORDINATE GEOMETRY Trapezoid EFGH has vertices E(–8, 4), F(–4, 8), G(8, 4) and H(–4, –8). Find the image of trapezoid EFGH after a dilation centered at the origin with a scale factor of Sketch the preimage and the image. Lesson 5 Ex3

Hint: If you did it right… Answer: E'(–2, 1), F'(–1, 2), G'(2, 1), Dilations in the Coordinate Plane Answer: E'(–2, 1), F'(–1, 2), G'(2, 1), H'(–1, –2) Hint: If you did it right… Lesson 5 Ex3

COORDINATE GEOMETRY Triangle ABC has vertices A(–1, 1), B(2, –2), and C(–1, –2). Find the image of ΔABC after a dilation centered at the origin with a scale factor of 2. Sketch the preimage and the image. A. B. C. D. none of the above A B C D Lesson 5 CYP3

frame length photo length Scale Drawing Sharetta built a frame for a photograph that is 20 centimeters by 25 centimeters. The frame measures 40 centimeters by 50 centimeters. Which scale factor did she use? Find the scale factor. frame length photo length Simplify. Answer: Sharetta used a scale factor of 2 to build the frame. Lesson 5 Ex5

Ruben is making a scale drawing of the front of his house Ruben is making a scale drawing of the front of his house. His house is 48 feet wide and 30 feet high at its highest point. Ruben decides on a dilation reduction factor of What size poster board will he need to make a complete drawing? A. 19 in. by 26 in. B. 22 in. by 30 in. C. 20.5 in. by 28 in. D. 16 in. by 29 in. A B C D Lesson 5 CYP5

Homework: Pg 529: #1, 2, 6 – 8, 10 – 19 all, 26 – 32 even.

Identify Scale Factor A. Determine the scale factor used for the dilation with center C. Determine whether the dilation is an enlargement, reduction, or congruence transformation. 6 2 Lesson 5 Ex4

D. 1; congruence transformation A. For the green preimage, determine the scale factor used for each dilation with center C. Determine whether the dilation is an enlargement, reduction, or congruence transformation. A. 2; enlargement B. C. D. 1; congruence transformation A B C D Lesson 5 CYP4

B. For the green preimage, determine the scale factor used for each dilation with center C. Determine whether the dilation is an enlargement, reduction, or congruence transformation. A. 2; enlargement B. C. D. 3; enlargement A B C D Lesson 5 CYP4