Image of a point in a line:

Assume that the the given line be ax + by + c = 0 and we have to find image of the point P(α, β).

Working rule:

Step 1: Find the equation of line PP' (where P' is image of P). Slope of PP' will be b/a, as PP' is perpendicular to given line. Thus equation of PP' is 

Step 2: Find the point of intersection of line PP' with the given line and let it be R(p, q). Visibly R is the mid point of PP'.

Step 3: Now 

Also                    

Thus the image is (2p - α, 2q -β)

Illustration: Find image of (5, 7) about line x -y + 6 = 0

Solution:                slope of line PP' =  -1

                              Therefore equation of PP'

                              y - 7 = - 1 (x - 5)  => x + y - 12 = 0

                              Point of intersect of x + y - 12 = 0 with x - y + 6 = 0 is (3, 9).

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