Point DD is located at left parenthesis, 2, comma, 1, right parenthesis(2,1) on the coordinate plane. Point DD is reflected over the yy-axis to create point D, primeD

Question

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. Point D, primeD
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is then reflected over the xx-axis to create point D, start superscript, prime, prime, end superscriptD
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. What ordered pair describes the location of D, start superscript, prime, prime, end superscript, question markD
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?

Answer 1

To find the location of point \( D'' \) after reflecting point \( D \) twice, we can follow these steps:

1. Start with point \( D = (2, 1) \).

2. Reflect over the y-axis: When reflecting a point \( (x, y) \) over the y-axis, the x-coordinate changes sign, while the y-coordinate remains the same. Therefore, reflecting \( D(2, 1) \) over the y-axis gives us: \[ D' = (-2, 1) \]

3. Reflect over the x-axis: Next, we reflect point \( D' \) over the x-axis. When reflecting a point \( (x, y) \) over the x-axis, the y-coordinate changes sign, while the x-coordinate remains the same. Therefore, reflecting \( D'(-2, 1) \) over the x-axis gives us: \[ D'' = (-2, -1) \]

So the ordered pair that describes the location of \( D'' \) is: \[ \boxed{(-2, -1)} \]