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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`
Name or write equations for the lines `L_1` and `L_2`

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To find the equations for the lines \( L_1 \) and \( L_2 \) based on the given invariant points, we can follow these steps: ### Step 1: Identify the Invariant Points for Line \( L_1 \) The points given are \( (3, 0) \) and \( (-1, 0) \). ### Step 2: Determine the Nature of the Line \( L_1 \) Since both points lie on the x-axis (where \( y = 0 \)), we can conclude that the line \( L_1 \) is the x-axis itself. ### Step 3: Write the Equation for Line \( L_1 \) The equation of the x-axis is: \[ y = 0 \] Thus, the equation for line \( L_1 \) is: \[ \text{Equation of } L_1: y = 0 \] ### Step 4: Identify the Invariant Points for Line \( L_2 \) The points given are \( (0, -3) \) and \( (0, 1) \). ### Step 5: Determine the Nature of the Line \( L_2 \) Both points lie on the y-axis (where \( x = 0 \)), indicating that the line \( L_2 \) is the y-axis itself. ### Step 6: Write the Equation for Line \( L_2 \) The equation of the y-axis is: \[ x = 0 \] Thus, the equation for line \( L_2 \) is: \[ \text{Equation of } L_2: x = 0 \] ### Final Answer: - Equation of line \( L_1 \): \( y = 0 \) - Equation of line \( L_2 \): \( x = 0 \) ---
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