Guided Problem Solving
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1 -1 Guided Problem Solving GPS Student Page 57, Exercises 1 1: Match each rule with the correct translation. A. (x, y) (x, y 1 ) I. P(, 1) P (3, ) B. (x, y) (x 1 3, y) II. Q(3, 0) Q (3, ) C. (x, y) (x 1, y 5) III. R(, ) R (1, ) 1. What are you asked to do?. Use the words left or right and up or down to describe the movement between each point and its image. Be sure to give the number of units each coordinate is translated. Point P(, 1) to P (3, ) Point Q(3, 0) to Q (3, ) Point R(, ) to R (1, ) 3. Which movements are written as addition?. Which movements are written as subtraction? 5. Match each rule with its translation. A 5 B 5 C 5. How could you check your answers? 7. Match each rule with the correct translation. A. (x, y) (x 3, y ) I. P(5, ) P (5, 5) B. (x, y) (x 1, y 1 ) II. Q(1, ) Q (5, ) C. (x, y) (x, y 3) III. R(, ) R (7, ) 3 Course 3 Lesson - Guided Problem Solving
2 - Guided Problem Solving GPS Student Page, Exercise : a. Graph the image of #JKL after it is reflected over the line m. Name the coordinates of #J K L. What do you notice about the y-coordinates? b. Translate #J K L to the left 3 units. Name the coordinates of #J K L. 1. Across what line will you reflect #JKL?. How many units to the left will you translate #JKL? 3. Write the coordinates for each vertex of #JKL. Point J Point K Point L y m J O L K x. Graph the reflected figure and name the new coordinates. Point J Point K Point L 5. Compare the y-coordinates of each vertex in Steps 3 and. What do you notice?. Translate the reflected figure 3 units to the left and name the new coordinates. Point J Point K Point L 7. What is the line of symmetry in your reflection? Compare the x-coordinates of Point J and Point J. What is their difference? m C B. Draw the reflection of #ABC with vertices A(1, 0), B(3, ), and C(, 3) across the y-axis. Give the coordinates of the reflection s vertices. A 3 Course 3 Lesson - Guided Problem Solving
3 -3 Guided Problem Solving GPS Student Page 7, Exercise 1: Graph #JKL with vertices J(1, 3), K(, ), and L(, ). Graph the three images formed by rotating the triangle 90, 10, and 70 about the origin. Give the coordinates of the vertices of each image. 1. What are you asked to do?. Around what point will the triangle be rotated? 3. Graph the triangle.. What is a rotation? 5. What direction does the figure rotate?. Rotate the figure 90 and mark each vertex. 7. Rotate the original figure 10 and mark each vertex.. Rotate the original figure 70 and mark each vertex. 9. How can you check that your figures are rotated correctly?. a. Graph #ABC with vertices A(, ), B(1, 1), and C(1, 3). b. Draw the three images formed by rotating the triangle 90, 10, and 70 about the origin. O 5 y 3 1 x O Course 3 Lesson -3 Guided Problem Solving
4 - Guided Problem Solving Transformations and Congruence GPS Student Page 7, Exercise :. Rectangle PQRS is transformed to rectangle P Q R S as shown on the graph. a. Describe a sequence of transformations to map rectangle PQRS to rectangle P Q R S. b. Identify all congruent line segments and angles. c. Can you perform a sequence of translations, reflections, or rotations on rectangle PQRS to produce a second rectangle that is not congruent to the first? Explain. 1. What are you being asked to describe? y S R Q P Q x O P R S. What are you being asked to identify? 3. List the corresponding line segments.. To map rectangle PQRS onto rectangle P Q R S should you start by translating, reflecting, or rotating rectangle PQRS? What transformation should you perform second? 5. Is it possible to produce a second rectangle that is not congruent to the first? Explain.. Graph and label a right triangle in the coordinate plane. Describe a sequence of transformations. Then draw and label the final transformation image. Give the coordinates of the vertices of both the original triangle and its final transformation image. 0 Course 3 Lesson - Guided Problem Solving
5 -5 Guided Problem Solving GPS Student Page 0, Exercise 1: Computers A window on a computer screen is 1 1 in. high and in. wide. After you click the size reduction button, the window is reduced to 1 1 in. high and 11 in. wide.what is the scale factor? 1. Place circles around the heights of the window and squares around the widths of the window.. What are you being asked to find? 3. Use the width dimension to find the scale factor by placing the values in the formula image original.. Simplify the fraction to find the scale factor. 5. Use the height dimension to find the scale factor. Does the value match your answer to Step?. A picture frame has an opening that is 1 in. by 15 in. If a matting is placed inside the frame to create an opening that is 7 1 in. by 93 in., what is the scale factor of the reduction? Course 3 Lesson -5 Guided Problem Solving
6 - Guided Problem Solving GPS Student Page 5, Exercise 13: A translation units down followed by a dilation with scale factor 1 maps #ABC onto #A B C. If AB 5 units, what is the length of A B? 1. What is a translation?. What is a dilation? 3. What is a scale factor?. What are you asked to determine in the problem? 5. Let #A B C be the image after the translation but before the dilation. What is the length of A B after a translation of #ABC units down? Explain your answer.. What is the length of A B after a dilation of #A B with a scale factor of 1? Explain your answer. 7. Draw a triangle with a side length of units on a coordinate grid. Then translate and dilate it according to the directions to check your answer.. A reflection across the y-axis is followed by a dilation with scale factor 1 maps #ABC onto #A B C. If AB 5 15 units, 3 what is the length of A B? Course 3 Lesson - Guided Problem Solving
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