Describing Transformations - Pre Algebra

1. Which transformations preserve both size and shape?

   Translations, reflections and rotations (the rigid motions). A dilation changes size unless its scale factor is 1.

2. What does a dilation do to a figure?

   It enlarges or shrinks the figure by a scale factor from a center. Shape and angles stay the same; size changes.

3. What is the image of $(2, 5)$ after a $90^\circ$ counterclockwise rotation about the origin?

   $(-5, 2)$. The rule is $(x, y) \to (-y, x)$.

4. What does a reflection do to a figure?

   It flips the figure over a line; each point and its image are the same distance from that line.

5. What is the image of $(2, 5)$ after a $180^\circ$ rotation about the origin?

   $(-2, -5)$. A $180^\circ$ rotation about the origin changes the sign of both coordinates.

6. What does a translation do to a figure?

   It slides every point the same distance in the same direction. Size, shape and orientation stay the same.

7. Which single transformation maps every point $(x, y)$ to $(-x, y)$?

   A reflection across the y-axis.

8. What is the image of $(4, 7)$ after a reflection across the y-axis?

   $(-4, 7)$. Reflecting across the y-axis changes the sign of $x$.

9. What is the image of $(3, -2)$ after a translation 4 units left and 5 units up?

   $(-1, 3)$. Subtract 4 from $x$ and add 5 to $y$.

10. Which single transformation maps every point $(x, y)$ to $(x + 3, y - 2)$?

    A translation 3 units right and 2 units down.

11. What is the image of $(4, 7)$ after a reflection across the x-axis?

    $(4, -7)$. Reflecting across the x-axis changes the sign of $y$.

12. What does a rotation do to a figure?

    It turns the figure through a given angle about a fixed point, the center of rotation.

Study these flashcards