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 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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