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Chapter - 12

Reflection

Reflection : -

A point P' is said to be the image of P in a straight line l, where l is the perpendicular bisector of the line segment PP'; The transformation which carries P to P' is called reflection and the straight line l is called the mirror line or mediator. The line l is called Me. Me (P) = P'

I. Reflection of a point in the x- axis.

To find the reflection of P (x , y) in x- axis a line PR perpendicular to x- axis is drawn and produced to P’ such that PR is equal to RP'. Then P’ is called the image of P under reflection in x- axis. If coordinates of P` be (x’, y’) then x’ = x and y’ = –y

Mx (P) = P

Mx (x, y) = (x', y') = (x, -y)

II. Reflection of a Point in the y- axis:

Let P(x, y) be a point whose reflection in y- axis is P` (-x, y).

My (P) = P'

My (x, y) = (-x, y)

III. Reflection through the origin.

When the point P(x, y) is reflected through the origin OP = OP`, PL and P` N are perpendicular on x-axis.

Mo (P) = P'

Mo (x, y) = (x', y')

= (-x, -y)

Reflection of a point in the origin is also known as half turn.