Question:
The equation of the image of the line $ 2y - x = 1 $ obtained by the reflection on the line $ 4y - 2x = 5 $ is:
The equation of the image of the line $ 2y - x = 1 $ obtained by the reflection on the line $ 4y - 2x = 5 $ is:
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To reflect a line across another, use the reflection formula, or apply the perpendicular bisector method to obtain the reflected line's equation.
Updated On: Apr 15, 2025
- \( 2y - x = 4 \)
- \( 2x - y = 4 \)
- \( 2y + x = 4 \)
- \( 2x + y = 4 \)
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The Correct Option is A
Solution and Explanation
Step 1:
The reflection of a line across another line involves finding the line's perpendicular bisector and applying the reflection formula. Here, we are reflecting the line \( 2y - x = 1 \) across the line \( 4y - 2x = 5 \).
Step 2:
The general method for reflecting a line involves using the reflection formula, which results in the new equation being: \[ 2y - x = 4 \]
Step 3:
Therefore, the equation of the image of the line \( 2y - x = 1 \) after reflection across \( 4y - 2x = 5 \) is \( 2y - x = 4 \).
The reflection of a line across another line involves finding the line's perpendicular bisector and applying the reflection formula. Here, we are reflecting the line \( 2y - x = 1 \) across the line \( 4y - 2x = 5 \).
Step 2:
The general method for reflecting a line involves using the reflection formula, which results in the new equation being: \[ 2y - x = 4 \]
Step 3:
Therefore, the equation of the image of the line \( 2y - x = 1 \) after reflection across \( 4y - 2x = 5 \) is \( 2y - x = 4 \).
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