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Lesson Menu Five-Minute Check (over Lesson 9–5) NGSSS Then/Now Key Concept: Dilation Example 1:Draw a Dilation Example 2:Real-World Example: Find the Scale of a Dilation Key Concept: Dilations in the Coordinate Plane Example 3:Dilations in the Coordinate Plane

Over Lesson 9–5 A.A B.B C.C D.D 5-Minute Check 1 A.yes; 4 lines B.yes; 3 lines C.yes; 2 lines D.This figure does not have line symmetry. State whether the figure appears to have line symmetry. If so, how many lines of symmetry does it have?

Over Lesson 9–5 1.A 2.B 3.C 5-Minute Check 2 A.yes; 8 lines B.yes; 4 lines C.yes; 2 lines D.This figure does not line symmetry. State whether the figure appears to have line symmetry. If so, how many lines of symmetry does it have?

Over Lesson 9–5 A.A B.B C.C D.D 5-Minute Check 3 A.5; 72 B.5; 45 C.6; 60 D.6; 72 The figure has rotational symmetry. State the order and magnitude of symmetry.

Over Lesson 9–5 A.A B.B C.C D.D 5-Minute Check 4 A.8; 60 B.8; 45 C.10; 45 D.10; 36 The figure has rotational symmetry. State the order and magnitude of symmetry.

Over Lesson 9–5 A.A B.B C.C D.D 5-Minute Check 5 A.order 2, magnitude 180 B.order 3, magnitude 120 C.order 6, magnitude 60 D.order 12, magnitude 30 What is the order and magnitude of symmetry of a regular hexagon?

NGSSS MA.912.G.2.4 Apply transformations to polygons to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent to the original shape. Create and verify tessellations of the plane using polygons. MA.912.G.2.6 Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform transformations in the plane.

Then/Now You identified dilations and verified them as similarity transformations. (Lesson 7–6) Draw dilations. Draw dilations in the coordinate plane.

Concept

Example 1 Draw a Dilation Copy trapezoid PQRS and point C. Then use a ruler to draw the image of trapezoid PQRS under a dilation with center C and scale factor 3. Since the dilation is an enlargement of trapezoid PQRS. Draw. Since r is negative, P', Q', R', and S' will lie on the opposite side of point C.

Example 1 Draw a Dilation Since the dilation is an enlargement of trapezoid PQRS. Locate P', Q', R', and S' so that Copy trapezoid PQRS and point C. Then use a ruler to draw the image of trapezoid PQRS under a dilation with center C and scale factor 3.

Example 1 Draw a Dilation Answer: Draw trapezoid P'Q'R'S'. Copy trapezoid PQRS and point C. Then use a ruler to draw the image of trapezoid PQRS under a dilation with center C and scale factor 3. Since the dilation is an enlargement of trapezoid PQRS.

A.A B.B C.C D.D Example 1 Which diagram shows the dilation image of ΔLMN with center C and ? A.B. C.D.

Example 2 Find the Scale Factor of a Dilation PUPPETS To create the illusion of a “life-sized” image, puppeteers sometimes use a light source to show an enlarged image of a puppet projected on a screen or wall. Suppose that the distance between a light source L and the puppet is 24 inches (LP). To what distance PP' should you place the puppet from the screen to create a 49.5-inch tall shadow (I'M') from a 9-inch puppet?

Example 2 Find the Scale Factor of a Dilation UnderstandThis problem involves a dilation. The center of the dilation is L, LP = 24 in., IM = 9 in., I'M' = 49.5 in. You are asked to find PP'. PlanFind the scale factor of the dilation from the preimage IM to the image I'M'. Use the scale factor to find LP and then use LP and LP' to find PP'.

Example 2 Find the Scale Factor of a Dilation SolveThe scale factor k of the enlargement is the ratio of the length on the image to a corresponding length on the preimage. Scale factor of image image = I'M', preimage = IM Divide.

Example 2 Find the Scale Factor of a Dilation Use this scale factor of 5.5 to find LP'. LP'=k(LP)Definition of dilation =5.5(24)k = 5.5 and LP = 24 =132Multiply. Use LP' and LP to find PP'. LP + PP'=LP' Segment Addition 24 + PP'=132LP = 24 and LP' = 132 PP'=108Subtract 24 from each side.

Example 2 Find the Scale Factor of a Dilation Answer: So, the puppet should be placed so that the distance from it to the screen (PP') is 108 inches. CheckSince the dilation is an enlargement, the scale factor should be greater than 1. Since 5.5 > 1, the scale factor is reasonable.

A.A B.B C.C D.D Example 2 A.100 inches B.180 inches C.220 inches D.240 inches PUPPETS Suppose you have a similar situation with the puppet and light source. The distance between the light source L and the puppet is 30 inches (LP). To what distance should you place the puppet from the screen to create a 54-inch tall shadow (I'M') from a 6-inch puppet?

Concept

Example 3 Dilations in the Coordinate Plane Trapezoid EFGH has vertices E(–8, 4), F(–4, 8), G(8, 4) and H(–4, –8). Graph the image of EFGH after a dilation centered at the origin with a scale factor of Multiply the x- and y-coordinates of each vertex by the scale factor,

Example 3 Dilations in the Coordinate Plane Graph the preimage and image. Answer: E'(–2, 1), F'(–1, 2), G'(2, 1), H'(–1, –2)

A.A B.B C.C D.D Example 3 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

End of the Lesson