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) →
(y, x))
(x,y) right arrow(y, x))

(x,y) →
(x, y)
(x,y) right arrow(x, y)

(x,y) →
(-x, -y)
(x,y) right arrow(-x, -y)

(x,y) →
(-y, -x)

Answer 1

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

A 180° rotation around the origin transforms a point \((x, y)\) to \((-x, -y)\).

Let's apply this rule to the point P(7, -2):

- The x-coordinate changes from 7 to -7.
- The y-coordinate changes from -2 to 2.

Thus, the transformation is:

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

The correct response is:

\[
(x,y) \rightarrow (-x, -y) \quad (x,y) \text{ right arrow } (-x, -y)
\]