• 41 questions

Translations, Rotations and Reflections Quiz

Find where a point lands after a slide, a flip or a turn.

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Every point of a triangle moves 4 units right and 2 units up. Which transformation is this?

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Unofficial practice questions, not affiliated with any school, exam board or textbook publisher. Bank checked October 8, 2026.

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All 41 questions with answers

Which transformation 14

  • A figure is flipped across a line, giving its mirror image. Which transformation is this? Answer: Reflection. Source: Wolfram MathWorld, Reflection. Read 2026-10-08.
  • A figure is reflected in a line, and its image is reflected in the same line. Where does it end up? Answer: Exactly where it started. Source: Wikipedia, Reflection (mathematics). Read 2026-10-08.
  • A figure is turned through an angle round a fixed point. Which transformation is this? Answer: Rotation. Source: Wolfram MathWorld, Rotation. Read 2026-10-08.
  • Every point of a triangle moves 4 units right and 2 units up. Which transformation is this? Answer: Translation. Source: Wikipedia, Translation (geometry). Read 2026-10-08.
  • The letter p is reflected in a vertical line. Which letter does its image look like? Answer: The letter q. Source: Wikipedia, Reflection (mathematics). Read 2026-10-08.
  • Triangle A(1, 1), B(4, 1), C(1, 3) is mapped to A′(1, −1), B′(4, −1), C′(1, −3). Which transformation does this? Answer: A reflection in the x-axis. Source: Wolfram MathWorld, Reflection. Read 2026-10-08.
  • Triangle A(1, 1), B(4, 1), C(1, 3) is mapped to A′(3, 4), B′(6, 4), C′(3, 6). Which transformation does this? Answer: A translation 2 units right and 3 units up. Source: Wolfram MathWorld, Translation. Read 2026-10-08.
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Which transformation, continued

  • Triangle A(1, 1), B(4, 1), C(1, 3) is mapped to A′(−1, 1), B′(−1, 4), C′(−3, 1). Which transformation does this? Answer: A rotation of 90° counterclockwise about the origin. Source: Wikipedia, Rotation matrix. Read 2026-10-08.
  • Triangle A(1, 1), B(4, 1), C(1, 3) is mapped to A′(−1, 1), B′(−4, 1), C′(−1, 3). Which transformation does this? Answer: A reflection in the y-axis. Source: Wolfram MathWorld, Reflection. Read 2026-10-08.
  • Triangle A(1, 1), B(4, 1), C(1, 3) is mapped to A′(−1, −1), B′(−4, −1), C′(−1, −3). Which transformation does this? Answer: A rotation of 180° about the origin. Source: Wikipedia, Point reflection. Read 2026-10-08.
  • The vertices A, B, C of a triangle run clockwise, but in its image A′, B′, C′ run counterclockwise. Which transformation was used? Answer: A reflection. Source: Wikipedia, Rigid transformation. Read 2026-10-08.
  • Which is true after any translation, reflection or rotation of a triangle? Answer: Its side lengths and angles are unchanged. Source: Wikipedia, Rigid transformation. Read 2026-10-08.
  • Which of these moves every point of the plane, leaving none where it was? Answer: A translation 3 units right. Source: Wikipedia, Rotation (mathematics). Read 2026-10-08.
  • Which transformation changes the size of a figure, so it is not a rigid transformation? Answer: Dilation. Source: Wolfram MathWorld, Dilation. Read 2026-10-08.

Translate a point 11

  • A translation follows the rule (x, y) → (x − 3, y + 2). Where does it send (4, −1)? Answer: (1, 1). Source: Wikipedia, Translation (geometry). Read 2026-10-08.
  • A translation maps A(1, 2) to A′(5, −1). Which translation is it? Answer: 4 units right and 3 units down. Source: Wikipedia, Translation (geometry). Read 2026-10-08.
  • A translation maps P(0, 1) to P′(3, 3). Where does the same translation send Q(−2, 4)? Answer: (1, 6). Source: Wikipedia, Translation (geometry). Read 2026-10-08.
  • A translation moves every point 3 units right and 4 units up. How far does each point move in a straight line? Answer: 5 units. Source: Wikipedia, Translation (geometry). Read 2026-10-08.
  • After a translation 5 units right and 1 unit down, the image of a point is (2, 2). Where was the point? Answer: (−3, 3). Source: Wikipedia, Translation (geometry). Read 2026-10-08.
  • The origin (0, 0) is translated by the vector (−2, 7). Where is its image? Answer: (−2, 7). Source: Wolfram MathWorld, Translation. Read 2026-10-08.
  • The point (1, 1) is translated 2 units right and 3 units up, then 4 units left and 1 unit down. Where does it end up? Answer: (−1, 3). Source: Wikipedia, Translation (geometry). Read 2026-10-08.
  • The point (2, 3) is translated 4 units right and 1 unit up. Where is its image? Answer: (6, 4). Source: Wolfram MathWorld, Translation. Read 2026-10-08.
  • The point (−1, 5) is translated 3 units left and 2 units down. Where is its image? Answer: (−4, 3). Source: Wolfram MathWorld, Translation. Read 2026-10-08.
  • Triangle ABC has its vertex B at (3, 0). The triangle is translated 2 units left and 4 units up. Where is B′? Answer: (1, 4). Source: Wolfram MathWorld, Translation. Read 2026-10-08.
  • Which rule moves every point 3 units right and 2 units down? Answer: (x, y) → (x + 3, y − 2). Source: Wikipedia, Translation (geometry). Read 2026-10-08.

Reflect or rotate a point 16

  • A point is reflected in the x-axis, and its image is reflected in the y-axis. Which single transformation gives the same result? Answer: A rotation of 180° about the origin. Source: Wikipedia, Point reflection. Read 2026-10-08.
  • The point (0, 3) is reflected in the y-axis. Where is its image? Answer: (0, 3). Source: Wikipedia, Reflection (mathematics). Read 2026-10-08.
  • The point (0, 6) is rotated 270° counterclockwise about the origin. Where is its image? Answer: (6, 0). Source: Wikipedia, Rotation matrix. Read 2026-10-08.
  • The point (1, 4) is reflected in the line y = x. Where is its image? Answer: (4, 1). Source: Wikipedia, Reflection (mathematics). Read 2026-10-08.
  • The point (2, 5) is rotated 180° about the origin. Where is its image? Answer: (−2, −5). Source: Wikipedia, Point reflection. Read 2026-10-08.
  • The point (2, −5) is reflected in the x-axis. Where is its image? Answer: (2, 5). Source: Wolfram MathWorld, Reflection. Read 2026-10-08.
  • The point (3, 1) is rotated 90° counterclockwise about the origin. Where is its image? Answer: (−1, 3). Source: Wikipedia, Rotation matrix. Read 2026-10-08.
  • The point (3, 2) is reflected in the x-axis. Where is its image? Answer: (3, −2). Source: Wolfram MathWorld, Reflection. Read 2026-10-08.
  • The point (4, −2) is rotated 90° clockwise about the origin. Where is its image? Answer: (−2, −4). Source: Wikipedia, Rotation matrix. Read 2026-10-08.
  • The point (−4, 1) is reflected in the y-axis. Where is its image? Answer: (4, 1). Source: Wolfram MathWorld, Reflection. Read 2026-10-08.
  • Which point stays where it is under any rotation about the origin? Answer: (0, 0). Source: Wolfram MathWorld, Rotation. Read 2026-10-08.
  • Which rule reflects a point in the x-axis? Answer: (x, y) → (x, −y). Source: Wolfram MathWorld, Reflection. Read 2026-10-08.
  • Which rule reflects a point in the y-axis? Answer: (x, y) → (−x, y). Source: Wolfram MathWorld, Reflection. Read 2026-10-08.
  • Which rule rotates a point 90° counterclockwise about the origin? Answer: (x, y) → (−y, x). Source: Wikipedia, Rotation matrix. Read 2026-10-08.
  • Which rule rotates a point 180° about the origin? Answer: (x, y) → (−x, −y). Source: Wikipedia, Point reflection. Read 2026-10-08.
  • Which way does a rotation through a positive angle, such as +90°, turn a figure? Answer: Counterclockwise. Source: Wikipedia, Rotation (mathematics). Read 2026-10-08.

How this list was compiled: Questions, wrong choices and explanations were written for this site. Definitions and rules were checked on the page named in the question's source line: Wolfram MathWorld (Translation, Reflection, Rotation, Dilation), https://mathworld.wolfram.com/, and Wikipedia (Translation (geometry), Reflection (mathematics), Rotation (mathematics), Rotation matrix, Rigid transformation, Point reflection). All read 2026-10-08. Every image point was worked out from those rules and checked again, and each wrong choice was checked not to give the same image. Licence: own work

How it works

This translations, rotations and reflections quiz has 41 coordinate questions in three sets: name the transformation that maps one figure to another, translate a point, and reflect a point in an axis or rotate it about the origin.

Read the full guide

Three sets

Which transformation gives a triangle's vertices before and after and asks what moved it. Translate a point also works back from an image to its point. Reflect or rotate a point uses the x-axis, the y-axis, the line y = x and turns of 90°, 180° and 270° about the origin.

Coordinates, no grid

In this quiz, translations, rotations and reflections are all given as coordinates, with no figure on screen. Plotting the point on squared paper before choosing shows which way it moves.

  • Counterclockwise is the positive direction, so −90° is a quarter turn clockwise.
  • A 270° turn counterclockwise lands on the same point as a 90° turn clockwise.

Questions and answers

What are translations, rotations and reflections?

The three basic rigid transformations. A translation slides every point the same distance in the same direction, a reflection flips a figure across a line to its mirror image, and a rotation turns it about a fixed point. Side lengths and angles stay the same.

What is the rule for a 90 degree counterclockwise rotation?

About the origin, (x, y) goes to (−y, x), so (3, 1) lands on (−1, 3). A 90° clockwise turn sends (x, y) to (y, −x), and a 180° turn sends it to (−x, −y).

What is the rule for a reflection over the x-axis?

(x, y) goes to (x, −y): the x-coordinate stays and the y-coordinate changes sign. Over the y-axis the rule is (−x, y), and over the line y = x the two coordinates swap.

Is a dilation a rigid transformation?

No. A dilation makes a figure larger or smaller, so its lengths change. The image keeps the shape and the angles of the original, but not its size.

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