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The point (-2, 0) on reflection in a lin...

The point (-2, 0) on reflection in a line is mapped to (2, 0) and the point (5, -6) on reflection in the same line is mapped to (-5, -6).
State the name of the mirror line and write its equation.

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To solve the problem, we need to identify the mirror line based on the given points and their reflections. ### Step 1: Identify the original and reflected points We have two points: - Point P: (-2, 0) which reflects to P': (2, 0) - Point Q: (5, -6) which reflects to Q': (-5, -6) ### Step 2: Analyze the changes in coordinates For point P: - The x-coordinate changes from -2 to 2. - The y-coordinate remains the same (0). For point Q: - The x-coordinate changes from 5 to -5. - The y-coordinate remains the same (-6). ### Step 3: Determine the nature of the reflection In both cases, we observe that the x-coordinates change signs while the y-coordinates remain unchanged. This indicates that the reflection is occurring across the y-axis. ### Step 4: State the name of the mirror line Since the reflection is across the y-axis, we can state that the mirror line is the y-axis. ### Step 5: Write the equation of the mirror line The equation of the y-axis is given by: \[ x = 0 \] ### Final Answer The mirror line is the y-axis, and its equation is \( x = 0 \). ---
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