MHB [ASK] Reflection of a Line by Another Line

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The discussion focuses on finding the reflection of the line 5x - 7y - 13 = 0 across the line y = -x. Participants explore substituting y = -x and x = -y into the original line equation. The correct reflection is determined to be 7x + 5y - 13 = 0. The contributor expresses surprise at the complexity of this problem compared to others. The conversation highlights the importance of understanding line reflections in geometry.
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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.
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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