Math Practice Problems - Transformations

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Transformations - 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=1, Mode=rot

Complexity=1, Mode=refl

Complexity=1, Mode=mix

Complexity=2, Mode=rot

Complexity=2, Mode=refl

Answers

Complexity=1, Mode=trans

#	Problem	Correct Answer	Your Answer
1	Figure out the translation components, and then where point P' ends up:	Translation: ( ,) Let P = (3, -4). P' = ( ,)
Solution To figure out the translation vector, pick a labeled point and subtract the old coordinates from the new. For example, Translation A'(-1, -2) - A (-4, -1) ------------- (3, -1) P' = P(3, -4) + (3, -1) -------------- (6, -5)

#	Problem	Correct Answer	Your Answer
2	Figure out the translation components, and then where point P' ends up:	Translation: ( ,) Let P = (-1, 3). P' = ( ,)
Solution To figure out the translation vector, pick a labeled point and subtract the old coordinates from the new. For example, Translation A'(-1, 2) - A (1, 4) ------------- (-2, -2) P' = P(-1, 3) + (-2, -2) -------------- (-3, 1)

Complexity=1, Mode=rot

#	Problem	Correct Answer	Your Answer
1		The transformation ABCD → A'B'C'D' is a rotation around (0, 0) by ° Rotate P around (0, 0) by the same angle. (You may need to sketch things out on paper.) P' = ( ,)
Solution Each point has been rotated around (0, 0) by -90°, which is also 270°. A(0, 1) → A'(1, -0) P(-2, -4) → P'(-4, 2) 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 4, since P(-2, -4) is 2 from pivot (0, 0) in the x direction and 4 from it in the y direction.

#	Problem	Correct Answer	Your Answer
2		The transformation ABCD → A'B'C'D' is a rotation around (0, 0) by ° Rotate P around (0, 0) by the same angle. (You may need to sketch things out on paper.) P' = ( ,)
Solution Each point has been rotated around (0, 0) by 180°. A(1, 1) → A'(-1, -1) P(0, 1) → P'(-0, -1) P is 1 in the y direction from the pivot. Rotating by 180 puts it at P'(-0, -1).

Complexity=1, Mode=refl

#	Problem	Correct Answer	Your Answer
1		Transformation ABCD → A'B'C'D' is a reflection across the x-axis y-axis Reflect P over the same line. (You may need to sketch things out on paper.) P' = ( ,)
Solution The line of reflection is y = 0, the x-axis. P is at (2, 0). Since the line of reflection is y = 0, 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 x-axis y-axis Reflect P over the same line. (You may need to sketch things out on paper.) P' = ( ,)
Solution The line of reflection is y = 0, the x-axis. P is at (-4, -1). Since the line of reflection is y = 0, reflecting a point comes down to switching the x and y coordinates.

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 translated by (-1, -3).

#	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 x-axis.

Complexity=2, Mode=rot

#	Problem	Correct Answer	Your Answer
1		The transformation ABCD → A'B'C'D' is a rotation around (1, -1) by ° Rotate P around (1, -1) by the same angle. (You may need to sketch things out on paper.) P' = ( ,)
Solution Each point has been rotated around (1, -1) by 180°. A(-8, 6) → A'(10, -8) P(0, 10) → P'(2, -12) 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 11, since P(0, 10) is 1 from pivot (1, -1) in the x direction and 11 from it in the y direction.

#	Problem	Correct Answer	Your Answer
2		The transformation ABCD → A'B'C'D' is a rotation around (3, 1) by ° Rotate P around (3, 1) by the same angle. (You may need to sketch things out on paper.) P' = ( ,)
Solution Each point has been rotated around (3, 1) by -90°, which is also 270°. A(7, -1) → A'(1, -3) P(-10, 8) → P'(10, 14) 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 13 and 7, since P(-10, 8) is 13 from pivot (3, 1) in the x direction and 7 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, 9). 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 The reflection is across x = -3. P is at (4, 4). P' is at (_, 4). Figure out the x-coordinate of P' by mirroring the distance (7) on the other side of the line.

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