Five-Minute Check (over Lesson 9–5)

CCSS

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. 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

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

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. 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. 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. 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. 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. 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. 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?

Over Lesson 9–5

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?

Content Standards

G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

G.SRT.1 Understand similarity in terms of similarity transformations. Verify experimentally the properties of dilations given by a center and a scale factor:

a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

Mathematical Practices

1 Make sense of problems and persevere in solving them.

5 Use appropriate tools strategically.

You identified dilations and verified them as similarity transformations.

• Draw dilations.

• Draw dilations in the coordinate plane.

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 k > 1, the dilation is an enlargement of trapezoid PQRS.

Draw a Dilation

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.

Draw a Dilation

Answer:

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.

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.

Which diagram shows the dilation image of ΔLMN

with center C and ?

A. B.

C. D.

Which diagram shows the dilation image of ΔLMN

with center C and ?

A. B.

C. D.

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?

Find the Scale Factor of a Dilation

Understand This 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'.

Plan Find 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'.

Find the Scale Factor of a Dilation

Solve The 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.

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

= 132 Multiply.

Use LP' and LP to find PP'.

LP + PP' = LP' Segment Addition

24 + PP' = 132 LP = 24 and LP' = 132

PP' = 108 Subtract 24 from each side.

Find the Scale Factor of a Dilation

Answer:

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.

Check Since the dilation is an enlargement, the scale factor should be greater than 1. Since 5.5 > 1, the scale factor is reasonable.

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?

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?

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,

Dilations in the Coordinate Plane

Graph the preimage and image.

Answer:

Dilations in the Coordinate Plane

Graph the preimage and image.

Answer: E'(–2, 1), F'(–1, 2), G'(2, 1), H'(–1, –2)

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

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