Study Guide - Chapter 6
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1 8 th Grade Name Date Period Study Guide - Chapter 6 1) Label each quadrant with I, II, III, or IV. 2) Use your knowledge of rotations to name the quadrant that each point below will land in after the rotation has been performed. All rotations are about the origin. You do not have to perform the rotation! Point A after a 180 rotation Point B after a 180 rotation Point C after a 180 rotation Point A after a 90 clockwise rotation Point B after a 90 clockwise rotation Point C after a 90 clockwise rotation
2 Point A after a 90 counter-clockwise rotation Point B after a 90 counter-clockwise rotation Point C after a 90 counter-clockwise rotation 3) A 270 clockwise rotation results in the same image as a rotation. A 270 counter-clockwise rotation results in the same image as a rotation. 4) Name the transformations that can prove congruency (the rigid transformations). Name the transformation that can prove similarity. 5) Match the symbol to its correct meaning. A. ~ B. Congruent Similar State TRUE or FALSE for problems Answer without actually performing the transformation. 6) After a 132 clockwise rotation about the origin, 45
3 P R R Q. 7) After a 132 clockwise rotation about the origin, PR P R. 8) Segment R Q will be 7 units long after a translation of (x+2, y+5) is performed on PQR followed by a reflection across the y-axis. 9) Segment R Q will be 3 units long after a translation of (x+2, y+5) is performed on PQR followed by a reflection across the y-axis. 10) Angle Q will be congruent to Angle Q after PQR is rotated 180 about point (-3, 1). 11) Angle R will be 45 after PQR is reflected across the x-axis. Triangle RST has vertices R(-7, -6), S(-5, -3) and T(1, -5). 12) If triangle RST is reflected across the y-axis, what will be the coordinates of the image? 13) If triangle RST is dilated by a scale factor of 3, what will be the coordinates of the image? 14) If triangle RST is rotated 270 clockwise about the origin, what will be the coordinates of the image?
4 15) Which sequence of transformations takes A to its image, B? A. translation 2 units down and 90 clockwise rotation about the origin. B. translation 12 units right and 90 clockwise rotation about the origin. C. reflection over the x-axis and translation 2 units down. D. reflection over the y-axis and translation 2 units down. Perform the sequence of transformations indicated to create a congruent figure called Figure 2. 16) 17) Translate right 10 and then Rotate 90 clockwise Rotate 180 clockwise and then Reflect over the y-axis
5 18) Reflect across the y-axis. 19) The coordinates for the vertices of ABC are listed below. What are the coordinates of the new image if the triangle is rotated 180 about the origin? A(2, -1) B(4, -3) C(5, -1) 20) Rotate 270 counter-clockwise. Pre-image Coordinates A(, ) B(, ) C(, ) Image Coordinates A (, ) B (, ) C (, )
6 21) Translate (x, y) (x + 8, y 2) A B List the coordinates of A B C D. A (, ) B (, ) C (, ) D (, ) C D 22) Rectangle EFGH was dilated using a scale factor of 3, then rotate 90 clockwise resulting in figure E F G H (not shown). What are the coordinates of E after the sequence of transformations?
7 23) 24) Triangle A undergoes a dilation with a scale factor of 0.5 and then is translated 5 units right resulting in Triangle B. Are the figures congruent or similar? Explain. 25)
8
9 8 th Grade Name Answer Key Date Period Study Guide - Chapter 6 1) Label each quadrant with I, II, III, or IV. 2) Use your knowledge of rotations to name the quadrant that each point below will land in after the rotation has been performed. All rotations are about the origin. You do not have to perform the rotation! Point A after a 180 rotation III Point B after a 180 rotation III Point C after a 180 rotation IV Point A after a 90 clockwise rotation IV Point B after a 90 clockwise rotation IV Point C after a 90 clockwise rotation I
10 Point A after a 90 counter-clockwise rotation II Point B after a 90 counter-clockwise rotation II Point C after a 90 counter-clockwise rotation III 3) A 270 clockwise rotation results in the same image as a 90 counter-clockwise rotation. A 270 counter-clockwise rotation results in the same image as a 90 clockwise rotation. 4) Name the transformations that can prove congruency (the rigid transformations). Answer: Translations, Reflections, Rotations Name the transformation that can prove similarity. Answer: Dilation 5) Match the symbol to its correct meaning. A. ~ B. B A Congruent Similar
11 State TRUE or FALSE for problems Answer without actually performing the transformation. 6) After a 132 clockwise rotation about the origin, P R R Q. FALSE 45 7) After a 132 clockwise rotation about the origin, PR P R. TRUE 8) Segment R Q will be 7 units long after a translation of (x+2, y+5) is performed on PQR followed by a reflection across the y-axis. FALSE 9) Segment R Q will be 3 units long after a translation of (x+2, y+5) is performed on PQR followed by a reflection across the y-axis. TRUE 10) Angle Q will be congruent to Angle Q after PQR is rotated 180 about point (-3, 1). TRUE 11) Angle R will be 45 after PQR is reflected across the x-axis. FALSE Triangle RST has vertices R(-7, -6), S(-5, -3) and T(1, -5). 12) If triangle RST is reflected across the y-axis, what will be the coordinates of the image? Answer: R (7, -6) S (5, -3) T(-1, -5)
12 13) If triangle RST is dilated by a scale factor of 3, what will be the coordinates of the image? Answer: R (-21, -18) S (-15, -9) T (3, -15) 14) If triangle RST is rotated 270 clockwise about the origin, what will be the coordinates of the image? Answer: R (6, -7) S (3, -5) T (5, 1) 15) Which sequence of transformations takes A to its image, B? A. translation 2 units down and 90 clockwise rotation about the origin. B. translation 12 units right and 90 clockwise rotation about the origin. C. reflection over the x-axis and translation 2 units down. D. reflection over the y-axis and translation 2 units down.
13 Perform the sequence of transformations indicated to create a congruent figure called Figure 2. 16) 17) Translate right 10 and then Rotate 90 clockwise Rotate 180 clockwise and then Reflect over the y-axis 18) Reflect across the y-axis
14 19) The coordinates for the vertices of ABC are listed below. What are the coordinates of the new image if the triangle is rotated 180 about the origin? A(2, -1) A (-2, 1) B(4, -3) B (-4, 3) C(5, -1) C (-5, 1) 20) Rotate 270 counter-clockwise. Pre-image Coordinates Image Coordinates A(, -7 ) 8 A ( 8, ) 7 B(, -2 ) 2 B (, ) 2 2 C(, -7 ) 2 C (, 2 ) 7
15 21) Translate (x, y) (x + 8, y 2) A B List the coordinates of A B C D. A ( 1-6, ) B (, ) 4-6 C (, 0-9 ) 5-9 D (, ) C D 22) Rectangle EFGH was dilated using a scale factor of 3, then rotate 90 clockwise resulting in figure E F G H (not shown). What are the coordinates of E after the sequence of transformations? Answer: E (-3, 9)
16 23) Answer:.5 or 1/2 24) Triangle A undergoes a dilation with a scale factor of 0.5 and then is translated 5 units right resulting in Triangle B. Are the figures congruent or similar? Explain. Answer: Similar because a dilation results in a figure that is the same shape but a different size.
17 25)
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Prerequisite Skills This lesson requires the use of the following skills: understanding that rigid motions maintain the shape and size of angles and segments, and that rigid motions include the transformations