Math Practice Problems - Transformations 2

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Transformations 2 - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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Complexity=2, Mode=rot

Complexity=2, Mode=refl

Complexity=3, Mode=trans

Complexity=3, Mode=rot

Complexity=3, Mode=refl

Answers

Complexity=1, Mode=mix

#	Problem	Correct Answer	Your Answer
1		What type of transform takes ABCD to A'B'C'D'? Translation Rotation Reflection
Solution Each point has been reflected across the y-axis.

#	Problem	Correct Answer	Your Answer
2		What type of transform takes ABCD to A'B'C'D'? Translation Rotation Reflection
Solution Each point has been reflected across the y-axis.

Complexity=2, Mode=rot

#	Problem	Correct Answer	Your Answer
1		The transformation ABCD → A'B'C'D' is a rotation around (-1, 2) by ° Rotate P around (-1, 2) by the same angle. (You may need to sketch things out on paper.) P' = ( ,)
Solution Each point has been rotated around (-1, 2) by 180°. A(-1, 9) → A'(-1, -5) P(-6, -7) → P'(4, 11) Since this is a rotation by an increment of 90°, we can figure out P' graphically by forming a right triangle with its hypotenuse connecting the pivot and point P. This should make it easy to draw the rotated P'. Your before and after triangles should both have legs of length 5 and 9, since P(-6, -7) is 5 from pivot (-1, 2) in the x direction and 9 from it in the y direction.

#	Problem	Correct Answer	Your Answer
2		The transformation ABCD → A'B'C'D' is a rotation around (-1, -3) by ° Rotate P around (-1, -3) by the same angle. (You may need to sketch things out on paper.) P' = ( ,)
Solution Each point has been rotated around (-1, -3) by 180°. A(7, 10) → A'(-9, -16) P(0, 7) → P'(-2, -13) Since this is a rotation by an increment of 90°, we can figure out P' graphically by forming a right triangle with its hypotenuse connecting the pivot and point P. This should make it easy to draw the rotated P'. Your before and after triangles should both have legs of length 1 and 10, since P(0, 7) is 1 from pivot (-1, -3) in the x direction and 10 from it in the y direction.

Complexity=2, Mode=refl

#	Problem	Correct Answer	Your Answer
1		Transformation ABCD → A'B'C'D' is a reflection across the line e.g. y=-3, y=x. Reflect P over the same line. (You may need to sketch things out on paper.) P' = ( ,)
Solution P is at (2, 5). Since the line of reflection is y = x, reflecting a point comes down to switching the x and y coordinates.

#	Problem	Correct Answer	Your Answer
2		Transformation ABCD → A'B'C'D' is a reflection across the line e.g. y=-3, y=x. Reflect P over the same line. (You may need to sketch things out on paper.) P' = ( ,)
Solution P is at (0, -2). Since the line of reflection is y = x, reflecting a point comes down to switching the x and y coordinates.

Complexity=3, Mode=trans

#	Problem	Correct Answer	Your Answer
1	All points are to be transformed by a translation of (-7, 7) followed by another translation of (10, -3).	Combined translation: ( ,) Let P = (8, 10). P'' = ( ,)
Solution To figure out the combined translation vector, add the individual vectors by component: (-7, 7) + (10, -3) ------------- (3, 4) P'' = P(8, 10) + (3, 4) --------------- (11, 14)

#	Problem	Correct Answer	Your Answer
2	All points are to be transformed by a translation of (2, -10) followed by another translation of (-3, 4).	Combined translation: ( ,) Let P = (6, 6). P'' = ( ,)
Solution To figure out the combined translation vector, add the individual vectors by component: (2, -10) + (-3, 4) ------------- (-1, -6) P'' = P(6, 6) + (-1, -6) --------------- (5, 0)

Complexity=3, Mode=rot

#	Problem	Correct Answer	Your Answer
1	All points are transformed by a rotation of 15° around (1, 1) followed by another rotation of 75° around the same point.	Combined angle of rotation around (1, 1): ° Rotate P around (1, 1) by the same angles. (You may need to sketch things out on paper.) P'' = ( ,)
Solution 15° + 75° = 90 Since this is a rotation by an increment of 90°, we can figure out P'' graphically by forming a right triangle with its hypotenuse connecting the pivot and point P. This should make it easy to draw the rotated P''. Your before and after triangles should both have legs of length 3 and 5, since P(4, -4) is 3 from pivot (1, 1) in the x direction and 5 from it in the y direction.

#	Problem	Correct Answer	Your Answer
2	All points are transformed by a rotation of 60° around (3, 3) followed by another rotation of 30° around the same point.	Combined angle of rotation around (3, 3): ° Rotate P around (3, 3) by the same angles. (You may need to sketch things out on paper.) P'' = ( ,)
Solution 60° + 30° = 90 Since this is a rotation by an increment of 90°, we can figure out P'' graphically by forming a right triangle with its hypotenuse connecting the pivot and point P. This should make it easy to draw the rotated P''. Your before and after triangles should both have legs of length 2 and 11, since P(5, -8) is 2 from pivot (3, 3) in the x direction and 11 from it in the y direction.

Complexity=3, Mode=refl

#	Correct Answer	Your Answer
1	Given a reflection across x = -3 , followed by a reflection across y = -x , the combined transformation is a translation rotation If this is a translation, give the translation components; if it is a rotation, give the coordinates of the pivot point: (),( )
Solution Two reflections along intersection lines results in a rotation around the intersection point (-3, 3). Solve the simple system of equations x = -3 y = -x to get the exact (x, y) coordinates. 1. 2.

#	Correct Answer	Your Answer
2	Given a reflection across y = 1 , followed by a reflection across y = -x , the combined transformation is a translation rotation If this is a translation, give the translation components; if it is a rotation, give the coordinates of the pivot point: (),( )
Solution Two reflections along intersection lines results in a rotation around the intersection point (-1, 1). Solve the simple system of equations y = 1 y = -x to get the exact (x, y) coordinates. 1. 2.

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