Analytic Geometry - Reflecting points over lines

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Let P = (5,1), and let Q be the reflection of P over the line y = 1/2x + 2. Find the coordinates of Q.

I don't understand how to start? Should we draw perpendicular lines?

  • Analytic Geometry - Reflecting points over lines -

    Given (x,y) and a line y = ax + c we want the point (x', y') reflected on the line.

    Set d:= (x + (y - c)*a)/(1 + a^2)

    Then x' = 2*d - x

    and y' = 2*d*a - y + 2c

    This relies on the fact the the distance from (h,k) to the line ax+by+c = 0 is

    |ah+bk+c|/√(a^2+b^2)

  • Analytic Geometry - Reflecting points over lines -

    thanks a lot

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