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Find the image of the point (4, -13) when reflected across the line 5x + y + 6 = 0.

1. (-1, -14)
2. (3, 4)
3. (1, 2)
4. (-4, 13)

Correct answer: (-1, -14)

Solution

Foot-of-perpendicular reflection: d=(5*4+(-13)+6)/(25+1)=13/26=1/2. Image x=4-2*5*(1/2)=-1, y=-13-2*1*(1/2)=-14. Image is (-1,-14).

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