Grade 8, Unit 1 Practice Problems - Open Up Resources

1 8/23/2017 Grade 8, Unit 1 Practice Problems - Open Up Lesson 1 Problem 1 The six frames show a shape's di erent how the shape moves to get from its position in each frame to the get from Position 1 to Position 2, the shape moves up. To get from Position 2 to Position 3, the shape rotates 90 degreescounterclockwise. To get from Position 3 to Position 4, the shape moves down and to the right. To get from Position 4 to Position 5 theshape rotates 90 degrees clockwise.

2 To get from Position 5 to Position 6, the shape moves to the : 90 degrees counterclockwise is the same as 270 degrees clockwise, and similarly 90 degrees clockwise is the same as 270 2 These ve frames show a shape's di erent how the shape moves to get from its position in each frame to the get from Position 1 to Position 2, the shape moves to the right. To get from Position 2 to Position 3, the shape rotates 90 degreesclockwise. To get from Position 3 to Position 4, the shape moves down. To get from Position 4 to Position 5, the shape rotates 3 Diego started with this Transformations and Congruence8/23/2017 Grade 8, Unit 1 Practice Problems - Open Up moves the shape down, turns it 90 degrees clockwise, then moves the shape to the right.

3 Draw the location of the shape aftereach 2 Problem 1 Each of the six cards shows a Which pair of cards shows a shape and its image after a rotation?2. Which pair of cards shows a shape and its image after a re ection?Solution1. Cards 1 and 42. Cards 3 and 5 Problem 2 The ve frames show a shape's di erent how the shape moves to get from its position in each frame to the 8/23/2017 Grade 8, Unit 1 Practice Problems - Open Up get from Position 1 to Position 2, the shape moves to the right. To get from Position 2 to Position 3, the shape ips over a horizontalline. To get from Position 3 to Position 4, the shape moves to the left. To get from Position 4 to Position 5, the shape ips over ahorizontal line again. The shape has then returned to its original position in Position , to get from Position 1 to Position 2 or from Position 3 to Position 4, the shape may ip over a vertical line.

4 Since the shapeis symmetric, a ip looks the same as a shift here. To get from Position 2 to Position 3 or from Position 4 to Position 5, the shape may berotated 180 degrees about a point not on the 3(from Unit 1, Lesson 1)The rectangle seen in Frame 1 is rotated to a new position, seen in Frame all the ways the rectangle could have been rotated to get from Frame 1 to Frame 40 degrees clockwiseB. 40 degrees counterclockwiseC. 90 degrees clockwiseD. 90 degrees counterclockwiseE. 140 degrees clockwiseF. 140 degrees counterclockwiseSolutionB, ELesson 3 Problem 1 Apply each transformation described to Figure A. If you get stuck, try using tracing A translation which takes to 2. A counterclockwise rotation of A, using center , of 60 degrees3. A re ection of A across line Solution1.

5 8/23/2017 Grade 8, Unit 1 Practice Problems - Open Up 3. Problem 2 Here is triangle drawn on a 8, Unit 1 Practice Problems - Open Up SolutionAnswers vary. Sample answers: The rotation is a 90-degree counterclockwise rotation using center . The translation is 4 units down and3 to the left. The re ection is across a horizontal line through point .Problem 3(from Unit 1, Lesson 2)1. Draw the translated image of so that vertex moves to . Tracing paper may be Draw the re ected image of Pentagon with line of re ection . Tracing paper may be Draw the rotation of Pentagon around clockwise by an angle of 150 degrees. Tracing paper and a protractor may 2. On the grid, draw a rotation of triangle , a translation of triangle , and a re ection of triangle.

6 Describe clearly how eachwas 8, Unit 1 Practice Problems - Open Up In the picture, angle measures 150 4 Problem 1 For each pair of polygons, describe a sequence of translations, rotations, and re ections that takes Polygon P to Polygon 2. 8/23/2017 Grade 8, Unit 1 Practice Problems - Open Up Solution1. Sample response: is translated to , followed by a rotation 60 degrees clockwise with center .2. Sample response: Polygon is re ected over line . is then translated to and a rotation of 60 degrees clockwise withcenter is Sample response: is translated to , then apply a rotation with center so that lands on top of . Finally the polygon isre ected over line .Problem 2(from Unit 1, Lesson 2)Here is quadrilateral and line .Draw the image of quadrilateral after re ecting it across line.

7 SolutionProblem 3(from Unit 1, Lesson 2)8/23/2017 Grade 8, Unit 1 Practice Problems - Open Up is quadrilateral .Draw the image of quadrilateral after each rotation using as 90 degrees clockwise2. 120 degrees clockwise3. 30 degrees counterclockwiseSolutionLesson 5 Problem 11. Here are some are the coordinates of , , and after a translation to the right by 4 units and up 1 unit? Plot these points on the grid, andlabel them , and .2. Here are some 8, Unit 1 Practice Problems - Open Up are the coordinates of , , and after a re ection over the axis? Plot these points on the grid, and label them , and .3. Here are some are the coordinates of , , and after a rotation about by 90 degrees clockwise? Plot these points on the grid, andlabel them , and.

8 Solution1. 2. , , 3. , , 8/23/2017 Grade 8, Unit 1 Practice Problems - Open Up 2(from Unit 1, Lesson 4)Describe a sequence of transformations that takes trapezoid A to trapezoid vary. Sample response: Translate A up, then rotate it 60 degrees counter-clockwise (with center of rotation the bottom vertex),and then translate it 3(from Unit 1, Lesson 3)Re ect polygon using line .SolutionLesson 6 Problem 1 Here is Trapezoid A in the coordinate plane:8/23/2017 Grade 8, Unit 1 Practice Problems - Open Up Draw Polygon B, the image of A, using the -axis as the line of re Draw Polygon C, the image of B, using the -axis as the line of re Draw Polygon D, the image of C, using the -axis as the line of re D is the same as B: re ecting a polygon twice over the -axis returns it to its original 2 The point is rotated 180 degrees counterclockwise using center.

9 What are the coordinates of the image?a. b. c. d. SolutionCProblem 3 Describe a sequence of transformations for which Triangle B is the image of Triangle 8, Unit 1 Practice Problems - Open Up vary. Sample response: B is the image of A under a re ection over the -axis, then a translation 2 units to the right and 2 4(from Unit 1, Lesson 2)Here is quadrilateral .Draw the image of quadrilateral after each The translation that takes to .2. The re ection over segment .3. The rotation about point by angle , Image of trapezoid moved to the left so that lines up with 2. Image of trapezoid sharing segment with 3. Image of trapezoid rotated so that the side corresponding to is now part of segment Lesson 7 Problem 1Is there a rigid transformation taking Rhombus P to Rhombus Q?

10 Explain how you , because the angle measures of the two polygons are di erent, and a rigid transformation must preserve all lengths and 2 Describe a rigid transformation that takes Triangle A to Triangle 8, Unit 1 Practice Problems - Open Up three units right and two units 3Is there a rigid transformation taking Rectangle A to Rectangle B? Explain how you know. SolutionNo, because the side lengths of the two rectangles are di erent, and a rigid transformation must preserve all lengths and 4(from Unit 1, Lesson 4)For each shape, draw its image after performing the transformation. If you get stuck, consider using tracing Translate the shape so that goes to .2. Rotate the shape 180 degrees counterclockwise around .8/23/2017 Grade 8, Unit 1 Practice Problems - Open Up 2.