Point WW is located at left parenthesis, 2, comma, 2, right parenthesis(2,2) on the coordinate plane. Point WW is reflected over the yy-axis to create point W, primeW

Question

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. Point W, primeW
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is then reflected over the xx-axis to create point W, start superscript, prime, prime, end superscriptW
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. What ordered pair describes the location of W, start superscript, prime, prime, end superscript, question markW
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?

Answer 1

To determine the location of point \( W'' \) after reflecting point \( W(2, 2) \) over the \( y \)-axis and then over the \( x \)-axis, we can follow these steps:

1. Reflect over the \( y \)-axis:

   • The reflection of a point \( (x, y) \) over the \( y \)-axis changes the sign of the \( x \)-coordinate, resulting in the point \( (-x, y) \).
   • For point \( W(2, 2) \): \[ W' = (-2, 2) \]

2. Reflect over the \( x \)-axis:

   • The reflection of a point \( (x, y) \) over the \( x \)-axis changes the sign of the \( y \)-coordinate, resulting in the point \( (x, -y) \).
   • For point \( W'(-2, 2) \): \[ W'' = (-2, -2) \]

Thus, the ordered pair that describes the location of \( W'' \) is

\[ \boxed{(-2, -2)} \]