The point P(-4, -5) on reflection in y-axis is mapped on P'. The point P' on reflection in the origin is mapped on 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 y-axis :

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

∴ Point P(-4, -5) becomes P'(4, -5) on reflection in y-axis.

We know that,

Rules to find the reflection of a point in the origin :

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

∴ Point P'(4, -5) becomes P''(-4, 5) on reflection in origin.

On reflecting the point P(-4, -5) in x-axis, it becomes (-4, 5) which are the coordinates of P''.

Hence, the single transformation that maps P(-4, -5) onto P''(-4, 5) is reflection of point P in x-axis.