Point GG is located at left parenthesis, 1, comma, 1, right parenthesis(1,1) on the coordinate plane. Point GG is reflected over the yy-axis to create point G, primeG

Question

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. Point G, primeG
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is then reflected over the xx-axis to create point G, start superscript, prime, prime, end superscriptG
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. What ordered pair describes the location of G, start superscript, prime, prime, end superscript, question markG
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?

Answer 1

To find the coordinates of point \( G'' \) after reflecting point \( G \) over first the \( y \)-axis and then the \( x \)-axis, we can follow these steps:

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

   • The coordinates of point \( G \) are \( (1, 1) \).
   • When a point \( (x, y) \) is reflected over the \( y \)-axis, the new coordinates become \( (-x, y) \).
   • Therefore, reflecting point \( G \) gives us: \[ G' = (-1, 1) \]

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

   • Now we take the coordinates of point \( G' \), which are \( (-1, 1) \).
   • When a point \( (x, y) \) is reflected over the \( x \)-axis, the new coordinates become \( (x, -y) \).
   • Thus, reflecting point \( G' \) gives us: \[ G'' = (-1, -1) \]

So, the ordered pair that describes the location of \( G'' \) is \( (-1, -1) \).