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The line y = x - 2 is turned about the point where it meets the x-axis until it becomes perpendicular to the line ax + by + c = 0. What is the resulting equation of the line?

1. (a + b)y + 2a = 0
2. ax - by - 2a = 0
3. bx + ay - 2b = 0
4. ay - bx + 2b = 0

Correct answer: ay - bx + 2b = 0

Solution

y=x-2 meets the x-axis at (2,0). Perpendicular to ax+by+c=0 (slope -a/b) needs slope b/a. The line through (2,0) with slope b/a is bx - ay - 2b = 0, i.e. ay - bx + 2b = 0.

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