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Point P (a, b) is reflected in the x-axi...

Point P (a, b) is reflected in the x-axis to P' (5,-2). Write down the values of a and b.

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To find the values of \( a \) and \( b \) for the point \( P(a, b) \) that is reflected in the x-axis to the point \( P'(5, -2) \), we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Reflection in the x-axis**: When a point \( P(x, y) \) is reflected in the x-axis, the x-coordinate remains the same, while the y-coordinate changes its sign. Therefore, the reflection of point \( P(a, b) \) in the x-axis will be \( P'(a, -b) \). 2. **Set Up the Reflection Equation**: According to the problem, the reflected point \( P' \) is given as \( (5, -2) \). Thus, we can write the following equations based on the reflection: \[ a = 5 \] \[ -b = -2 \] 3. **Solve for \( a \)**: From the first equation, we directly find: \[ a = 5 \] 4. **Solve for \( b \)**: From the second equation, we can solve for \( b \): \[ -b = -2 \implies b = 2 \] 5. **Final Values**: Therefore, the values of \( a \) and \( b \) are: \[ a = 5, \quad b = 2 \] ### Summary: The values of \( a \) and \( b \) are: - \( a = 5 \) - \( b = 2 \)
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