Middle School Math Quiz: Describing Transformations
4 questions · exam conditions
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Describing TransformationsQuestion 1 of 4

Figure ABCD is reflected across line mm to create figure A'B'C'D'. Then figure A'B'C'D' is reflected across line nn, where line nn is parallel to line mm and 5 units away from it. What single transformation is equivalent to these two reflections?

A rotation of 180° about the midpoint between lines mm and nn
A translation of 10 units in the direction perpendicular to both lines
A translation of 5 units in the direction perpendicular to both lines
A reflection across a line parallel to mm and nn and equidistant from them
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Middle School Math Quiz

Middle School Math Quiz: Describing Transformations

Practice Describing Transformations in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Describing Transformations, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Figure ABCD is reflected across line mm to create figure A'B'C'D'. Then figure A'B'C'D' is reflected across line nn, where line nn is parallel to line mm and 5 units away from it. What single transformation is equivalent to these two reflections?

  1. A rotation of 180° about the midpoint between lines mm and nn
  2. A translation of 10 units in the direction perpendicular to both lines (correct answer)
  3. A translation of 5 units in the direction perpendicular to both lines
  4. A reflection across a line parallel to mm and nn and equidistant from them
Explanation: When a figure is reflected across two parallel lines, the result is equivalent to a translation. The distance of translation is twice the distance between the parallel lines, in the direction from the first line to the second line. Since the lines are 5 units apart, the translation distance is 2 × 5 = 10 units. Choice A describes reflection across perpendicular lines, Choice C uses the wrong distance, Choice D would result in the original figure.

Question 2

A regular hexagon centered at the origin undergoes a dilation with scale factor 2, followed by a reflection across the x-axis. If a vertex of the original hexagon was at (3, 0), which statement correctly describes the combined transformation?

  1. The transformation is equivalent to a single reflection across the line y=−xy = -x
  2. The final image has a vertex at (6, 0) and the hexagon's orientation is reversed (correct answer)
  3. The final image has a vertex at (-6, 0) and the hexagon maintains its original orientation
  4. The final image has a vertex at (6, 0) and the hexagon maintains its original orientation
Explanation: First, dilation by scale factor 2: vertex (3, 0) → (6, 0). Then reflection across x-axis: (6, 0) → (6, 0) since it's on the x-axis. However, other vertices will show the orientation change. A reflection reverses orientation (clockwise ↔ counterclockwise). Choice A is incorrect as this isn't equivalent to reflection across y = -x, Choice C has wrong coordinates, Choice D incorrectly states orientation is maintained.

Question 3

A square with side length 4 is rotated 45° clockwise about its center, then dilated by scale factor 12\frac{1}{2} about the same center point. What is the area of the final image compared to a square with the same orientation as the original that circumscribes the final image?

  1. Final image area: 4; circumscribing square area: 8 (correct answer)
  2. Final image area: 4; circumscribing square area: 16
  3. Final image area: 8; circumscribing square area: 16
  4. Final image area: 2; circumscribing square area: 8
Explanation: Original square has area 16. After rotation, area stays 16 but orientation changes (becomes diamond-shaped relative to coordinate axes). After dilation by 1/2, area becomes 16 × (1/2)² = 4. The rotated square with side length 2 fits inside a square aligned with axes. The diagonal of the rotated square is 2√2, so the circumscribing axis-aligned square has side length 2√2 and area (2√2)² = 8. Choice B uses original area, Choice C uses pre-dilation area, Choice D has wrong calculation.

Question 4

A triangle is dilated by a scale factor of 3 with center at point C, which is one of the triangle's vertices. After dilation, the triangle is rotated 45° clockwise about the same point C. Which property of the triangle is preserved throughout both transformations?

  1. The measure of all three angles and the position of vertex C (correct answer)
  2. The length of all three sides and the position of vertex C
  3. The area of the triangle and the measure of all three angles
  4. The perimeter of the triangle and the position of vertex C
Explanation: Dilation preserves angle measures but changes side lengths by the scale factor (3). Since C is the center of dilation, point C doesn't move. Rotation preserves all distances and angles, and since C is the center of rotation, C remains fixed. Therefore, all angle measures and the position of vertex C are preserved. Choice B is wrong because dilation changes side lengths, Choice C is wrong because dilation changes area by factor of 9, Choice D is wrong because dilation changes perimeter by factor of 3.