Transformations and Congruence Quiz

Grade 8 · Math · Quiz

Test your knowledge of geometric transformations and congruence on the coordinate plane.

Questions

1. When a figure is reflected over the y-axis, what happens to the x-coordinates of each point?

   1. They stay the same
   2. They become negative of themselves
   3. They are multiplied by 2
   4. They are set to 0
   Show answer

   Answer: They become negative of themselves

   Reflecting over the y-axis changes (x, y) to (-x, y), negating the x-coordinate.

2. Which transformations always produce a congruent figure?

   1. Dilations only
   2. Translations, reflections, and rotations
   3. Dilations and translations
   4. Reflections and dilations
   Show answer

   Answer: Translations, reflections, and rotations

   These are rigid transformations that preserve size and shape, guaranteeing congruence.

3. Point B is at (-2, 5). After a 90° clockwise rotation about the origin, where is B'?

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

   Answer: (5, 2)

   For a 90° clockwise rotation: (x, y) → (y, -x). So (-2, 5) → (5, 2).

4. A triangle has vertices at (1,1), (3,1), and (2,3). After a translation of (0, -4), what are the new y-coordinates?

   1. -3, -3, -1
   2. 1, 1, 3
   3. -4, -4, -4
   4. 5, 5, 7
   Show answer

   Answer: -3, -3, -1

   Subtract 4 from each y-coordinate: 1-4=-3, 1-4=-3, 3-4=-1.

5. Which scale factor in a dilation would shrink a figure?

   1. 2
   2. 3/2
   3. 1
   4. 1/2
   Show answer

   Answer: 1/2

   A scale factor between 0 and 1 reduces the size of the figure.

6. Two figures are congruent if one can be mapped to the other using:

   1. A dilation
   2. Only a translation
   3. A sequence of rigid transformations
   4. A scale factor greater than 1
   Show answer

   Answer: A sequence of rigid transformations

   Congruence is defined by the ability to map one figure onto another using translations, reflections, and/or rotations.

7. A reflection always changes the orientation (order of vertices) of a figure.

   Show answer

   Answer: True

   A reflection reverses the orientation (e.g., clockwise becomes counterclockwise), which is a key property distinguishing it from other rigid transformations.

8. Reflecting point (4, -3) over the x-axis gives the point (4, _____).

   Show answer

   Answer: 3

   Reflecting over the x-axis changes (x, y) to (x, -y). So (4, -3) becomes (4, 3).

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