Question
What is the image of \( (5,-8) \) after a reflection over the \( x \)-axis?
Ask by Norris Norton. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The image of \((5, -8)\) after reflecting over the \( x \)-axis is \((5, 8)\).
Solution
1. The formula for reflecting a point \((x, y)\) over the \( x \)-axis is:
\[
(x, y) \to (x, -y)
\]
2. For the point \((5, -8)\), the \( x \)-coordinate remains the same and the \( y \)-coordinate becomes:
\[
-(-8) = 8
\]
3. Thus, the image of the point \((5, -8)\) after the reflection over the \( x \)-axis is:
\[
(5, 8)
\]
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Simplify this solution Extra Insights
When you reflect a point over the \( x \)-axis, the \( x \)-coordinate remains the same, while the \( y \)-coordinate changes its sign. Therefore, reflecting the point \( (5, -8) \) over the \( x \)-axis results in \( (5, 8) \). So, the image of \( (5, -8) \) after reflection over the \( x \)-axis is \( (5, 8) \).
