Question

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

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

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