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When an object is placed before a plane mirror, the image formed is at the same distance behind the mirror as the object is in front of it. Therefore, to find the image of a point P in line AB, consider AB as the plane mirror and point P as the object.
The reflection (or image) of a point P in line AB is a point P’ such that AB is the perpendicular bisector of the line segment PP’. Line AB is called the axis of reflection.
Relection of a point in a line:
(i) The reflection of the point P(x,y) in the xaxis i.e., y= 0 is the point P'(x, y)
(ii) The reflection of the point P(x,y) in the yaxis i.e., x = 0 is the point P'(x, y)
(iii) The reflection of the point P(x,y) in the line y = a is the point P'(x, y+2a)
(iv) The reflection of the point P(x,y) in the line x = a is the point P'(x+2a,y)
The reflection of the point P(x,y) in the origin is the point P'(x, y).
A point is called an invariant point with respect to a given line if and only if it lies on the line.
Some important results:
The line x = 0 is the yaxis.
The line y = 0 is the xaxis.
The line x = a is a line parallel to the yaxis at a distance ‘a’ from it.
The line y = b is a line parallel to the xaxis at a distance ‘b’ from it.
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