Question

An image is drawn of a figure. After a 180°
(counterclockwise) rotation about the origin, P(7,−2)
is mapped to P′(−7,2)
. Identify the rule that maps P
to P′
.(1 point)
Responses

(x,y)→(−x,−y)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative x comma negative y right parenthesis

(x,y)→(−x,y)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative x comma y right parenthesis

(x,y)→(x,−y)
left parenthesis x comma y right parenthesis right arrow left parenthesis x comma negative y right parenthesis

(x,y)→(y,x)

Answer 1

To find the rule that maps the point \( P(7, -2) \) to the point \( P'(-7, 2) \) after a 180° rotation about the origin, we can analyze the transformation.

When a point \( (x, y) \) is rotated 180° around the origin, the coordinates of the point transform as follows:

\[
(x, y) \rightarrow (-x, -y)
\]

Applying this rule to the point \( P(7, -2) \):

\[
(7, -2) \rightarrow (-7, -(-2)) = (-7, 2)
\]

This matches the point \( P'(-7, 2) \).

Thus, the correct mapping rule is:

\[
(x, y) \rightarrow (-x, -y)
\]

**Final Answer:**

\((x,y) \rightarrow (-x, -y)\)