Point UU is located at left parenthesis, 6, comma, 3, right parenthesis(6,3) on the coordinate plane. Point UU is reflected over the xx-axis to create point U, primeU

Question

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. Point U, primeU
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is then reflected over the yy-axis to create point U, start superscript, prime, prime, end superscriptU
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. What ordered pair describes the location of U, start superscript, prime, prime, end superscript, question markU
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?

Answer 1

To find the location of point \( U'' \) after reflecting point \( UU(6, 3) \) over the x-axis and then over the y-axis, let's follow these steps:

1. Reflect over the x-axis:

   • When a point \((x, y)\) is reflected over the x-axis, the new coordinates change to \((x, -y)\).
   • For point \( UU(6, 3) \), the reflection over the x-axis gives us: \[ U' = (6, -3) \]

2. Reflect over the y-axis:

   • When a point \((x, y)\) is reflected over the y-axis, the new coordinates change to \((-x, y)\).
   • For point \( U'(6, -3) \), the reflection over the y-axis yields: \[ U'' = (-6, -3) \]

Thus, the ordered pair that describes the location of point \( U'' \) is \((-6, -3)\).