Geometry Practice Test: Transformations (Translations, Reflections, Rotations, Dilations)
- Transformations
- 10 questions
- 12 minutes
Rotations are counterclockwise about the origin unless a question says otherwise. Tip: test a rule on an easy point such as (1, 0) before you trust it.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
Point (3, −5) is reflected over the x-axis. What are the coordinates of the image?
Correct answer: B
Reflecting over the x-axis keeps x and changes the sign of y: (3, 5). The point (−3, −5) is the reflection over the y-axis.
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Question 2
Point (4, 1) is rotated 90° counterclockwise about the origin. What are the coordinates of the image?
Correct answer: C
A 90° counterclockwise rotation maps (x, y) to (−y, x), so (4, 1) becomes (−1, 4). The point (1, −4) is the result of a clockwise rotation.
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Question 3
The translation (x, y) → (x − 3, y + 7) is applied to point (2, −4).
What are the coordinates of the image?
Correct answer: A
Subtract 3 from x and add 7 to y: (2 − 3, −4 + 7) = (−1, 3). The point (5, −11) applies both changes in the wrong direction.
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Question 4
Point (−2, 6) is reflected over the line y = x. What are the coordinates of the image?
Correct answer: D
Reflecting over y = x swaps the coordinates: (6, −2). The point (−6, 2) is the reflection over y = −x, and (2, −6) is a 180° rotation.
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Question 5
Point (4, 3) is dilated by a scale factor of 2 with center (1, 1).
What are the coordinates of the image?
Correct answer: B
From the center to the point is (3, 2); doubling gives (6, 4), and adding it to the center gives (7, 5). The point (8, 6) dilates about the origin instead of (1, 1).
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Question 6
A figure is reflected over the x-axis and then reflected over the y-axis.
Which single transformation has the same result?
Correct answer: C
The two reflections map (x, y) to (x, −y) and then to (−x, −y), which is the rule for a 180° rotation about the origin.
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Question 7
What is the smallest positive rotation about its center that maps a regular pentagon onto itself?
Correct answer: D
A regular pentagon has rotational symmetry of order 5, so the smallest rotation is 360°/5 = 72°. The value 108° is the interior angle of the pentagon.
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Question 8
Which transformation reverses the orientation of a figure (clockwise order of vertices becomes counterclockwise)?
Correct answer: B
A reflection produces a mirror image, so the order of the vertices is reversed. Translations, rotations and dilations with a positive scale factor all keep the orientation.
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Question 9
Which transformation is described by the rule (x, y) → (−y, x)?
Correct answer: A
Test the point (1, 0): it maps to (0, 1), a quarter turn counterclockwise. The clockwise rule is (x, y) → (y, −x), and a reflection over y = x only swaps the coordinates.
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Question 10
Point (5, −1) is reflected over the vertical line x = 2. What are the coordinates of the image?
Correct answer: C
The point is 3 units to the right of x = 2, so the image is 3 units to the left: x = 2 − 3 = −1, and y stays −1. The point (−5, −1) is the reflection over the y-axis.
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