Question

Match each of the descriptions with the correct rule for the transformation.

Question 1 options:


Translation 2 left and 2 up


Rotation 90° counterclockwise


Translation 2 right and 2 down


Reflection over the x-axis

1.
(x, y) → (-y, x)

2.
(x, y) → (x + 2, y – 2)

3.
(x, y) → (x, -y)

4.
(x, y) → (x – 2, y + 2)

Answer 1

Answer:

1.  Rotation 90° counterclockwise

    (x, y) → (-y, x)

2.  Translation 2 right and 2 down

    (x, y) → (x + 2, y – 2)

3.  Reflection over the x-axis

    (x, y) → (x, -y)

4.  Translation 2 left and 2 up

    (x, y) → (x – 2, y + 2)

Step-by-step explanation:

Translation 2 left and 2 up

To translate (move) a point two units to the left, we subtract 2 from its x-value.  Similarly, to translate (move) a point two units up, we add 2 to its y-value.

• (x, y) → (x – 2, y + 2)

Rotation 90° counterclockwise

When rotating a point 90° counterclockwise, the y-value becomes negative, and the x and y switch:

• (x, y) → (-y, x)

Translation 2 right and 2 down

To translate (move) a point two units to the right, we add 2 to its x-value.  Similarly, to translate (move) a point two units down, we subtract 2 from its y-value.

• (x, y) → (x + 2, y – 2)

Reflection over the x-axis

When a point is reflected over the x-axis, the y-value is negated but the x-value stays the same:

• (x, y) → (x, -y)