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Points (3, 0) and (-1,0) are invariant p...

Points (3, 0) and (-1,0) are invariant points under reflection in the line `L_1` points (0, -3) and (0, 1) are invariant points on reflection in line `L_2`
Write down the images of points P (3, 4) and Q (-5, -2) on reflection in `L_1` Name the images as P' and Q' respectively.

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To find the images of points P(3, 4) and Q(-5, -2) under reflection in the line L1, we first need to determine the nature of the line L1 based on the given invariant points. ### Step-by-step Solution: 1. **Identify the Invariant Points and the Line L1**: The points (3, 0) and (-1, 0) are invariant under reflection in line L1. Since both points lie on the x-axis (y = 0), we conclude that L1 is the x-axis itself. - **Equation of L1**: \( y = 0 \) 2. **Reflect Point P(3, 4) in Line L1**: To reflect a point across the x-axis, we keep the x-coordinate the same and change the sign of the y-coordinate. - Original point P: (3, 4) - Reflected point P': (3, -4) 3. **Reflect Point Q(-5, -2) in Line L1**: Similarly, for point Q, we again keep the x-coordinate the same and change the sign of the y-coordinate. - Original point Q: (-5, -2) - Reflected point Q': (-5, 2) 4. **Final Images**: - The image of point P is P' = (3, -4) - The image of point Q is Q' = (-5, 2) ### Summary of Results: - P' = (3, -4) - Q' = (-5, 2)
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