[ASK] Reflection of a Line by Another Line

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SUMMARY

The discussion centers on the mathematical problem of finding the reflection of the line represented by the equation 5x - 7y - 13 = 0 across the line y = -x. The correct reflection is identified as option A: 7x + 5y - 13 = 0. Participants engaged in deriving the reflection by substituting y = -x and x = -y into the original equation, confirming the transformation. The simplicity of the steps involved surprised the original poster, highlighting the importance of methodical problem-solving in geometry.

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Monoxdifly
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The reflection of the line 5x - 7y - 13 = 0 by the line y = -x is ...
A. 7x + 5y - 13 = 0
B. 7x + 5y + 13 = 0
C. 7x - 5y - 13 = 0
D. 7x - 5y + 13 = 0
E. 7y + 5x + 13 = 0

This one I totally have no idea. Like, at all.
 
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If we let:

$$y=-x$$

and

$$x=-y$$

in the given line, what do we obtain?
 
-5y + 7x - 13 = 0?
 
Monoxdifly said:
-5y + 7x - 13 = 0?

Correct. :)
 
I can't believe that out of the 4 questions I asked tonight, the one I found the hardest was the one with the simplest step.
 

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