Geometric Transformations Quiz

Grade 10 · Math · Quiz

Apply transformation rules and properties to solve coordinate and conceptual geometry problems.

Questions

1. Point P(−4, 3) is rotated 180° about the origin. What are the new coordinates?

   1. (4, −3)
   2. (−3, −4)
   3. (3, 4)
   4. (−4, −3)
   Show answer

   Answer: (4, −3)

   Rotation 180° about origin: (x, y) → (−x, −y). So (−4, 3) → (4, −3).

2. Which transformation preserves both shape and size?

   1. Rotation
   2. Dilation with k ≠ 1
   3. Dilation with k = 2
   4. Both dilation and rotation
   Show answer

   Answer: Rotation

   Rotation is a rigid motion (isometry) that preserves both shape and size. Dilation with k ≠ 1 changes size.

3. Triangle ABC is reflected over the line y = x. If A = (2, 5), what is A'?

   1. (5, 2)
   2. (−2, −5)
   3. (2, −5)
   4. (5, −2)
   Show answer

   Answer: (5, 2)

   Reflection over y = x swaps coordinates: (2, 5) → (5, 2).

4. A translation changes the orientation of a figure.

   Show answer

   Answer: False

   Translation slides every point by the same vector without rotating or flipping, so orientation is preserved.

5. A figure is dilated with scale factor ½ from the origin. The area of the image compared to the pre-image is:

   1. ¼ of the original
   2. ½ of the original
   3. Same as the original
   4. Double the original
   Show answer

   Answer: ¼ of the original

   Area scales by k² = (½)² = ¼.

6. Which pair of transformations will always produce a congruent image?

   1. Reflection followed by translation
   2. Dilation followed by reflection
   3. Dilation followed by rotation
   4. Dilation by factor 2 then factor 1/2
   Show answer

   Answer: Reflection followed by translation

   Both reflection and translation are rigid motions (isometries), so their composition also produces a congruent image.

7. What single transformation is equivalent to two successive reflections over parallel lines that are 3 cm apart?

   1. Translation by 6 cm
   2. Rotation by 180°
   3. Dilation by factor 2
   4. Reflection over a perpendicular line
   Show answer

   Answer: Translation by 6 cm

   Two reflections over parallel lines produce a translation of twice the distance between the lines: 2 × 3 = 6 cm.

8. A rotation of 270° counterclockwise about the origin maps (x, y) to (y, ______).

   Show answer

   Answer: -x

   270° CCW = 90° CW: (x, y) → (y, −x).

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