The point P(4, -7) on reflection in x-axis is mapped onto P'. Then P' on reflection in the y-axis is mapped onto P''. Find the coordinates of P' and P''. Write down a single transformation that maps P onto P''.

We know that,

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

1. Retain the abscissa i.e. x-coordinate.
2. Change the sign of ordinate i.e. y-coordinate.

∴ Coordinates of point P(4, -7) on reflection in x-axis is P'(4, 7).

We know that,

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

1. Change the sign of abscissa i.e. x-coordinate.
2. Retain the ordinate i.e. y-coordinate.

∴ Coordinates of point P'(4, 7) on reflection in y-axis is P''(-4, 7).

The single transformation that maps P(4, -7) onto P''(-4, 7) is reflection in the origin.