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 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)
left parenthesis x comma y right parenthesis right arrow left parenthesis y comma x right parenthesis

(x,y)→(−x,−y)

Answer 1

The transformation that maps point P(7, -2) to point P'(-7, 2) is a 180° rotation about the origin. The rule that describes this transformation is:

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

This means that both the x-coordinate and the y-coordinate are negated. Therefore, the correct response is:

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