Rotation, Reflection and Translation

Describe the Transformation

• Reflection

• Translation

• Rotation

Describe the Transformation

• Translation

• Rotation

• Reflection

What quadrant is the image now in?

• I

• II

• III

• IV

Translations are always _______

• Congruent

• Bigger

• Smaller

• Rotated

In the figure, triangle PQR has vertices P(0, −1), Q(3, −1) and R(5, −3). What are the vertices of the image after the translation (x, y) → (x − 5, y + 1)?

• P′ (1, −6), Q′ (4, −6), R′ (6, −8)

• P′ (−5, 0), Q′ (−2, 0), R′ (0, −2)

• P′ (5, −2), Q′ (8, −2), R′ (10, −4)

• P′ (−1, 4), Q′ (2, 4), R′ (4, 2)

Which reflection does the image show?

• Reflection across the x-axis according to the rule (x, y) → (x, −y)

• Reflection across the y-axis according to the rule (x, y) → (x, −y)

• Reflection across the x-axis according to the rule (x, y) → (−x, y)

• Reflection across the y-axis according to the rule (x, y) → (−x, y)

A reflection is applied to triangle ABC according to the rule (x, y) → (x, –y). Which of the following will describe the effect of the reflection?

• A′ will stay as the top vertex.

• C′ will now be the top vertex.

• C′ will stay as the bottom vertex.

• B′ will be the bottom vertex.

Triangle ABC is rotated 270° counterclockwise about the origin. Which is the algebraic rule applied to one of the vertices?

• (−1, −4) → (−4, 1)

• (−4, −1) → (−4 + 5, 1 + 3)

• (−4, 1) → (−1, −(−4))

• (−4, 1) → (1, −(−4))

Which rule would give the translation from point P (2, 5) to the image P′ (−1, 7)?

• Move 3 units left and 2 units up.

• Move 3 units right and 2 units up.

• Move 3 units left and 7 units up.

• Move 2 units right and 2 units up.

Square ABCD is translated by the rule (x – 3, y + 1). What are the coordinates of D′?

• (–2, 4)

• (4, 2)

• (0, 0)

• (–3, 4)