Question

what is the mapping rule for a 180 degree rotation about the origin?

(x, y) \
ightarrow (-y, x)
(x, y) \
ightarrow (-y, -x)
(x, y) \
ightarrow (-x, -y)
(x, y) \
ightarrow (x, -y)

Explanation:

Identify the transformation type

$$ \text{Rotation of } 180^\circ \text{ about the origin } (0,0). $$

Apply the coordinate rule

$$ (x, y) ightarrow (-x, -y) $$

Match with the given options

$$ \text{Option 3: } (x, y) ightarrow (-x, -y) $$

Answer:

• (A) \((x, y)

ightarrow (-y, x)\)

• (B) \((x, y)

ightarrow (-y, -x)\)

• **(C) \((x, y)

ightarrow (-x, -y)\) (Correct answer)**

• (D) \((x, y)

ightarrow (x, -y)\)