Chapter 11.5 Homework Practice Rotations on the Coordinate Plane

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1 Chapter 11.5 Homework Practice Rotations on the Coordinate Plane Draw each figure after the rotation described clockwise rotation about point A clockwise rotation about point A 3. A figure has vertices A(1, 3), B(1, 5), and C(5, 4). Graph the figure and its image after a rotation of 90 clockwise about the origin. Determine whether each figure has rotational symmetry. If it does, describe the angle of rotation Many countries have cooperated to build the International Space Station. The flags below represent three of them. a. Which flags have rotational symmetry? b. Describe the angle of rotation for each flag. Math Accelerated Chapter 11 Congruence, Similarity, and Transformations

2 Chapter 11.5 Problem-Solving Practice Rotations on the Coordinate Plane 1. Corinne noticed that hubcaps are a good source of objects that have rotational symmetry. One day she observed the four hubcaps shown below. Determine the angle of rotation for each hubcap. 2. If vertex U of quadrilateral STUV is located in Quadrant IV and the quadrilateral is rotated 180 clockwise about the origin, in what quadrant will vertex U' lie? 3. In Southern California, there are miles of three-bladed windmills that are used to produce electricity. Determine if the blades of the windmills have rotational symmetry. If so, describe the angle of rotation. 4. Examine each capital letter in the alphabet and determine which letters have rotational symmetry at Trapezoid ABCD is shown at the right. 6. Refer to the trapezoid in Exercise 5. Graph the trapezoid after a counterclockwise rotation of 270 about the origin. Graph the trapezoid after a clockwise rotation of 90 about the origin. What do you notice about the two images graphed in Questions 5 and 6?

3 Chapter 11.6 Problem-Solving Practice Congruence and Transformations 1. Two swimming pool designs are shown below. Are the two designs congruent? Use transformations to explain your reasoning. 2. Two flower beds are shown below. Are the two flower beds congruent? Use transformations to explain your reasoning. 3. The community softball team has created the following logo for their jerseys. What transformations could be used if the letter M is the image and the letter W is the preimage? Are the two figures congruent? Explain. 4. For the local art gallery opening, the curator had the design shown below created. What transformations could be used if white figure is the image and the black figure is the preimage? Are the two figures congruent? Explain. 5. For his school web page, Manuel created the logo shown at the below. What transformations could be used if the gray figure is the preimage and the black figure is the image? 6. Refer to the figures in Exercise 5. Are the two figures congruent? Explain.

4 Chapter 11.6 Enrich Using Coordinates For Exercises 1-4, use the coordinate plane at the right. 1. Graph the points (1, 1), (4, 4), and (2, 4). Connect the dots. Name the figure formed. 2. Multiply each y coordinate in Exercise 1 by 1. Graph the points. How is this triangle related to the one in Exercise 1? 3. Multiply each coordinate in Exercise 1 by 1. Graph the points. 4. What would you have to do to get the coordinates of a triangle in Quadrant II congruent to the ones in Exercises 1-3? For Exercises 5-10, use the coordinate plane at the right. 5. Graph the points (3, 1), (2, 3), (4, 6), and (5, 4). Connect the dots. The figure formed is called a parallelogram. 6. Add 2 to both coordinates of each point and graph the new coordinates. Name the figure formed. 7. Add 4 to the x-coordinate of each point in Exercise 5 and graph the new coordinates. Is this figure also a parallelogram? 8. Graph the points (5, 2), (6, 3), (5, 5), and (3, 3) on the coordinate plane at the right. Name the figure formed. 9. Multiply both coordinates of each point in Exercise 8 by 2 and graph the new coordinates. This is an enlargement. 10. Multiply both coordinates of each point in Exercise 8 by and graph the new coordinates. This is a reduction.

5 Chapter 11.7 Homework Practice Dilations on the Coordinate Plane Find the vertices of each figure after a dilation with the given scale factor k. Then graph the image. 1. k = 3 2. k = k = 4. k = 5. Find the vertices of figure STUV after a dilation with a scale factor of 1.5 if it has vertices S( 4, 1), T( 4, 6), U( 2, 8), and V( 2, 3). Then graph the image. 6. Jordan has a photo of a lion that is 4 inches by 6 inches. He wants to sketch a larger version of the photo on paper that is 14 inches by 21 inches. What is the scale factor of the dilation? 7. Mrs. Williamson is projecting a slide on the wall. The image on the slide is 1.25 inches by 1.5 inches. The image projected on the wall is 20 inches by 24 inches. What is the scale factor of the dilation?

6 Chapter 11.7 Problem-Solving Practice Dilations on the Coordinate Plane 1. A parallelogram has vertices at A( 8, 5), B(10, 3), C(1, 5), and D( 4, 3). Find the coordinates of the figure after a dilation with a scale factor of Linda is sketching a triangular pennant on a piece of grid paper. The triangle s vertices are located at (1, 3), (1, 15), and (16, 9). Once she got the sketch the way she wanted, she drew a larger copy. Find the coordinates of the triangle after a dilation with a scale factor of Rita enlarged a picture on a photocopier. The original photo was 3.5 by 5 inches. The copy was 8.75 by 12.5 inches. What is the scale factor of the dilation? 4. Mike had a photo made into a postage stamp. The photo was 7 by 9.5 inches and the stamp was 1.4 by 1.9 inches. What is the scale factor of the dilation? 5. An ad agency designed a logo for a company. The logo is shown below. Each square on the grid represents 1 square inch. 6. Refer to the diagram in Exercise 5. The company wants to enlarge the logo for t-shirts. What would the coordinates of the vertices of the outer edge of the figure be after a dilation with a scale factor of 1.5? The company wants to create a smaller version of the logo to use on their letterhead. Graph the dilation of the logo with a scale factor of.

7 Chapter 11.8 Homework Practice Similarity and Transformations Determine if the two figures are similar by using transformations. Explain your reasoning Jenna is creating a mural for her bedroom wall. She would like to copy a picture that is 2 inches by 2.5 inches. She uses a copy machine to enlarge it by a factor of 4. Then she projects it on her wall at a factor of 12. What are the dimensions of the mural? Are the pictures similar? 6. Mr. Fletcher is looking at a 0.5 millimeter section of plant under a microscope. The plant section appears enlarged by a scale factor of 10 when looking through the microscope. He uses the camera on the microscope to photograph what is seen through the lenses at a scale factor of 20. What is the length of the section of plant in the photograph? Chapter 11.8 Problem-Solving Practice

8 Similarity and Transformations 1. Stephanie has a photo of her family that she is placing in a frame. The original photo is 5 inches by 7 inches. She enlarges the photo by a scale factor of 2 to place in her room. She then enlarges this photo by a scale factor of 1.5 to place above her fireplace. What are the dimensions of the photo above her fireplace? Are the enlarged photos similar to the original? 2. An architect is designing a decorative window. The window uses similar parallelograms. If parallelogram ABEG is similar to parallelogram ACDF, what is the length AF? 3. An iron-on measures 3 inches by 4 inches. It is enlarged by a scale factor of 2 for a t-shirt. The second iron-on is an enlargement of the t-shirt iron-on by a scale factor of 3. What are the dimensions of the largest iron-on? Are both of the enlarged iron-ons similar to the original? 4. Casey is reducing the size of her painting to make it into a postcard. The painting is 12 inches by 20 inches. She will reduce it by a scale factor of. What are the dimensions of the postcard? 5. Ryan is using tiles in his bathroom. He chooses 1-inch by 2-inch tiles for the border and would like tiles that are similar to the border as the interior tiles. The interior tiles will be larger by a scale factor of 3.5. What are the dimensions of the interior tiles? 6. For an art show, an artist is projecting a piece of art 5 inches by 7 inches onto a white wall. It will be enlarged by a scale factor of 12. What are the dimensions of the art on the wall?