An image is drawn of a figure. After a 180 degree (counterclockwise) rotation about the origin, P (7, -2) is mapped to P' (-7, 2). Identify the rule that maps P to P'.

Question

a. (x, y) -> (y, x)
b. (x, y) -> (x, y)
c. (x, y) -> (-x, -y)
d. (x, y) -> (-y, -x)

Answer 1

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

A 180-degree rotation about the origin takes a point (x, y) and transforms it to (-x, -y).

Given:

• Original point P: (7, -2)
• After rotation P': (-7, 2)

Now let's apply the transformation rule:

1. Start with point P:

   • P = (x, y) = (7, -2)

2. Apply the rule of rotation (for 180 degrees):

   • P' = (-x, -y) = (-7, 2)

This matches exactly with P' so the mapping rule is indeed: c. (x, y) → (-x, -y)

Therefore, the correct answer is:

c. (x, y) -> (-x, -y)