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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 1/23 Grade 8 Mathematics EOG (GSE) Quiz Answer Key Geometry - (MGSE8.G.3 ) Effect Of Transformations Student Name: _______________________ Date: _________ Teacher Name: THUYNGA DAO Score: _________ 1) If polygon ABCD is moved right 3 and up 2, what would the new coordinates of vertex D? A) (0, 9) B) (1, 0) C) (4, 2) D) (-3, 5) Explanation: If you move ABCD right 3 and up 2 you need to add three to the x-coordinates and 2 to the y-coordinates. Since the coordinates of vertex D are (-2, -2) then the new coordinates would be (0, 1). 2)
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 2/23 After rectangle WXYZ is translated 4 units to the left, what are the coordinates of X’? A) (-2, 2) B) (0, -3) C) (0, 2) D) (8, 2) Explanation: After translating the rectangle 4 units to the left, the coordinates of X’ are (0, 2). 3) If ΔMTV is reflected across the y-axis, what are the resulting coordinates of point M? A) (-2, 5) B) (-5, 2) C) (5, -2) D) (-2, -5) Explanation: Solution: (-2, 5). Reflecting the triangle across the y-axis will result in every x-coordinate becoming opposite. 4)
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 3/23 Point M is located at (3, 7). If point M is translated 2 units to the left and 4 units down, what are the coordinates of M’? A) (-1, 5) B) (1, 3) C) (5, 3) D) (7, 5) Explanation: (3 – 2 = 1, 7 – 4 = 3) The coordinates of M’ are (1, 3).
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 4/23 5) If ΔMTV is reflected across the x-axis, what are the resulting coordinates of point T? A) (5, 4) B) (-4, 5) C) (4, -5) D) (-5, -4) Explanation: Solution: (4, -5). Reflecting the triangle across the x-axis will result in every y-coordinate becoming opposite. 6) When the blue trapezoid is translated to the green one, the new coordinates of the point (-2, 8) will be A) (-4, 0). B) (-8, 0). C) (0, -8). D) (-4, -8). Explanation: (-8, 0) is correct. Imagine lifting the blue one up and dropping it onto the green one. 7)
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 5/23 If ΔABC is dilated by a scale factor of 2 with a dilation center of A, what will be the coordinates of point B'? A) (0, 0) B) (0, 3) C) (0, 4) D) (0, 6) Explanation: The solution is (0, 6). In the new triangle the side that corresponds to AB will be 6 units. Since the center is (0, 0), point B' will fall at point (0, 6). 8) If square HIJK is dilated by a scale factor of 1 3 with a dilation center of (0, 0), what will be the coordinates of point K'? A) (1, 1) B) (-1, 1) C) (1, -1) D) (0, -1) Explanation: The solution is (1, -1). To find the resulting coordinates of point K' multiply point K (3, -3) by the scale factor of 1 3 . The result is (1, -1)
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 6/23 9) Which graph shows the original figure rotated 180°? A) B) C)
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 7/23 D) Explanation: An image that has been rotated 180° will be diagonal from the original image. If it has been rotated 90° it will be directly beside the original image, 270° directly below the original image, and 360° directly on top of the original image. the correct image is 10)
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 8/23 Reflect pentagon ABCDE across the y-axis. What are the coordinates of B’? A) (-5, 3) B) (-4, 3) C) (-3, 2) D) (4, -3) Explanation: The coordinates of B are (4, 3). After reflecting across the y-axis, the coordinates of B’ are (-4, 3). 11) If rectangle DEFG is dilated by a scale factor of 3 with a dilation center of (0, 0), what will be the coordinates of point D'?
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 9/23 A) (-6, 0) B) (3, -2) C) (-6, -3) D) (-6, -2) Explanation: The solution is (-6, -3). To find the resulting coordinates of point D' multiply point D (-2, -1) by the scale factor of 3. The result is (-6, -3) 12) Triangle ABC has been dilated to triangle A'B'C'. Which factor was used? A) 1 B) 2 C) 3 D) 4 Explanation: 2 is correct. For example, the point C(2, 1) has been multiplied by 2 to become (4, 2), which is C'. 13)
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 10/23 If polygon ABCD is translated 4 units to the right, in which quadrant will vertex C be? A) I B) II C) IV D) III Explanation: If you move the polygon four units to the right vertex C will go from (-3, 7) to (1,7). The result is in quadrant I.
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 11/23 14) Find the coordinates of the vertices of the figure after the given transformation. translation: (x, y)→(x - 4, y + 4) A) J'(1, 0), N'(5, 0), M'(5, 3), P'(2, 5) B) J'(-2, 5), N'(2, 5), M'(2, 2), P'(-1, 0) C) J'(-3, 4), N'(1, 4), M'(1, 1), P'(-2, -1) D) J'(-1, 0), N'(-5, 0), M'(-5, -3), P'(-2, -5) Explanation: The rule (x, y)→(x - 4, y + 4), means to translate the figure four points to the left and four points up. If we apply this rule to each vertex of the figure, the resulting coordinates are J'(-3, 4), N'(1, 4), M'(1, 1), P'(-2, -1). 15)
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 12/23 Describe the transformation of ΔABC. A) rotation of 90° about the origin B) rotation of 60° about the origin C) rotation of 180° about the origin D) rotation of 270° about the origin Explanation: rotation of 180° about the origin The triangle rotates from Quadrant I to Quadrant III, which is 180°. 16)
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 13/23 Rotate trapezoid ABCD 90° clockwise around the origin. What are the coordinates of D’? A) (-4, 2) B) (4, -2) C) (0, 4) D) (4, 0) Explanation: The coordinates of D are (-4, 0). After rotating 90° clockwise around the origin, the coordinates of D’ are (0, 4). 17)
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 14/23 You are given rectangle ABCD on the grid shown and are told that the figure is reflected, but you are not told over which axis this has occurred. Which COULD be the new coordinates of point D? A) (4, -4) B) (-6, -4) C) (-2, -2) D) (-1, -4) Explanation: The coordinates of point D are (-4, -4). Look for coordinates that have the sign of either the x or the y coordinate changed but not both. Therefore the correct answer is (4, -4)
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 15/23 18) Which transformation will move polygon ABCD completely into one quadrant? A) up 5 units B) down 5 units C) left three units D) reflect over the x-axis Explanation: If you move ABCD up 5 units the points below the x-axis will move above the x-axis and the polygon will be in one quadrant. 19)
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 16/23 Triangle ABC has been dilated to triangle A'B'C'. Which factor was used? A) 0.5 B) 1.0 C) 1.5 D) 2.0 Explanation: 2 is correct. For example, the point C(2, 1) has been multiplied by 2 to become (4, 2), which is C'. 20) A rotation in the origin is shown. The angle of rotation appears to be A) 30°. B) 45°. C) 60°. D) 90°. Explanation: 90° is correct. If we compare one of the blue sides with its red image, we can see the 90-degree angle formed at the origin. 21)
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 17/23 If ΔABC is dilated by a scale factor of 1 2 with a dilation center of A, what will be the coordinates of point C'? A) (0, 0) B) (1, 0) C) (0, 1) D) (4, 0) Explanation: The solution is (1, 0). In the new triangle the side that corresponds to AC will be 1 unit. Since the center is (0, 0), point C' will fall at point (1, 0). 22)
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 18/23 A circle with a radius of 1 unit and center C at (-2, 1) is reflected across the x-axis. What are the coordinates of C’? A) (2, 1) B) (2, -1) C) (-2, 4) D) (-2, -1) Explanation: The coordinates of C are (-2, 1). After reflecting across the x-axis, the coordinates of C’ are (-2, -1).
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 19/23 23) You are given rectangle ABCD on the grid shown and are told that the figure is moved two units. The person fails to tell you in what direction. Which COULD be the new coordinates of point D? A) (4, -4) B) (-6, -4) C) (-2, -2) D) (-1, -4) Explanation: The coordinates of point D are (-4, -4). Look for coordinates that have 2 either added or subtracted from either the x or the y coordinate but not both. Therefore the correct answer is (-6, -4) 24) What kind of transformation does the graph show? A) flip B) rotation C) slide D) translation Explanation: It is a rotation around the origin. 25)
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 20/23 Find the coordinates of the vertices of the figure after the given transformation. reflection across the x-axis A) U'(0, 5), P'(-1, 0), R'(3, -1), D'(3, 2) B) U'(2, -4), P'(1, 1), R'(5, 2), D'(5, -1) C) U'(-1, 3), P'(-2, 2), R'(2, 3), D'(2, 0) D) U'(-4, -3), P'(-5, 2), R'(-1, 3), D'(-1, 0) Explanation: When we reflect across the x-axis, the resulting image will be a mirror image with the x-axis as the line of symmetry. Therefore, U'(0, 5), P'(-1, 0), R'(3, -1), D'(3, 2) are the correct coordinates. 26)
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 21/23 Find the coordinates of the vertices of the figure after the given transformation. reflection across the y-axis A) G'(4, 0), J'(3, -3), M'(0, -3) B) G'(-1, 2), J'(-2, 5), M'(-5, 5) C) G'(1, -2), J'(2, -5), M'(5, -5) D) G'(0, 2), J'(-1, -1), M'(-4, -1) Explanation: When we reflect across the y-axis, the resulting image will be a mirror image with the y-axis as the line of symmetry. Therefore, G'(1, -2), J'(2, -5), M'(5, -5) are the correct coordinates.
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 22/23 27) If Kite ABCD is reflected across the x-axis, what are the resulting coordinates of point A? A) (1, -3) B) (-3, 1) C) (3, -1) D) (-3, -1) Explanation: Solution: (-3, 1). Reflecting the kite across the x-axis will result in every y-coordinate becoming the opposite. 28) When the blue trapezoid is translated to the green one, the new coordinates of the point (0, 0) will be A) (-6, -2).
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4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 23/23 B) (-2, -8). C) (-8, -6). D) (-6, -8). Explanation: (-6, -8) is correct. Since the point (6, 8) ends up at (0, 0), we can see that we have to subtract 6 from the x and 8 from the y. Doing this to the point (0, 0) results in (-6, -8). 29) A triangle in Quadrant I is reflected twice, first over the y-axis and then over the x-axis. The new triangle, in Quadrant III, could ALSO have been obtained by using a single A) dilation. B) glide reflection. C) rotation. D) translation. Explanation: A counterclockwise rotation of 180° has the same effect as two reflections in perpendicular lines. 30) If rectangle DEFG is dilated by a scale factor of 1 2 with a dilation center of (0, 0), what will be the coordinates of point F'? A) (1, 1) B) (0, 1 2 ) C) ( 1 2 , 1) D) (1, 1 2 ) Explanation: The solution is (1, 1 2 ). To find the resulting coordinates of point F' multiply point F (2, 1) by the scale factor of 1 2 . The result is (1, 1