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Fill in the blanks : {:("Point","Trans...

Fill in the blanks :
`{:("Point","Transformation ","Image"),(.........., "Reflection in y - axis",(0,6)):}`

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To solve the problem, we need to find the original point \( P \) whose reflection in the y-axis is given as \( P' (0, 6) \). ### Step-by-step Solution: 1. **Understanding Reflection in the Y-axis**: - When a point \( P(x, y) \) is reflected in the y-axis, its x-coordinate changes sign while the y-coordinate remains the same. Thus, the reflection of point \( P \) will be \( P'(-x, y) \). 2. **Identify the Coordinates of the Image**: - We know that the image point \( P' \) is given as \( (0, 6) \). 3. **Set Up the Reflection Equation**: - According to the reflection property, if \( P' \) is \( (0, 6) \), then the original point \( P \) must satisfy: \[ P' = (-x, y) \implies (0, 6) = (-x, y) \] 4. **Solve for the Coordinates of Point \( P \)**: - From the equation \( (0, 6) = (-x, y) \), we can equate the coordinates: - For the x-coordinate: \[ -x = 0 \implies x = 0 \] - For the y-coordinate: \[ y = 6 \] 5. **Conclusion**: - Therefore, the coordinates of point \( P \) are \( (0, 6) \). ### Final Answer: The required point \( P \) is \( (0, 6) \). ---
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