Point WW is located at left parenthesis, 6, comma, minus, 3, right parenthesis(6,−3) on the coordinate plane. Point WW is reflected over the xx-axis to create point W, primeW

Question

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. Point W, primeW
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is then reflected over the yy-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 find the coordinates of point \( W'' \) after the successive reflections of point \( W \) over the \( x \)-axis and then over the \( y \)-axis, we will perform the transformations step by step.

1. Start with the coordinates of point \( W \): \[ W = (6, -3) \]

2. Reflecting over the \( x \)-axis: When a point \( (x, y) \) is reflected over the \( x \)-axis, the \( y \)-coordinate changes sign. Therefore, the reflection of \( W \) over the \( x \)-axis is calculated as follows: \[ W' = (6, -(-3)) = (6, 3) \]

3. Reflecting over the \( y \)-axis: Now, we reflect point \( W' \) over the \( y \)-axis. When a point \( (x, y) \) is reflected over the \( y \)-axis, the \( x \)-coordinate changes sign. Thus, the reflection of \( W' \) over the \( y \)-axis is: \[ W'' = (-6, 3) \]

Therefore, the ordered pair that describes the location of \( W'' \) is: \[ \boxed{(-6, 3)} \]