The point P(4, -7) is reflected in the origin to point P'. The point P' is then reflected in x-axis to the point P".

(i) Find the co-ordinates of P'.

(ii) Find the co-ordinates of P".

(iii) Write down a single transformation that maps P onto P".

(i) We know that,

Rule to find reflection of a point in origin :

Change the sign of abscissa and ordinate.

∴ Point P'(-4, 7) is the image of point P(4, -7) on reflection in origin.

Hence, P' = (-4, 7).

(ii) We know that,

Rule to find reflection of a point in x-axis :

Change the sign of ordinate i.e. y-coordinate.

Retain the abscissa i.e. x-coordinate.

∴ Point P"(-4, -7) is the image of point P'(-4, 7) on reflection in x-axis.

Hence, P" = (-4, -7).

(iii) P(4, -7) ⇒ P"(-4, -7)

A transformation that keeps the y-coordinate the same and changes the sign of the x-coordinate is a reflection in the y-axis.

Hence, single transformation that maps P into P" is reflection in the y-axis.