(i) Point P(a, b) is reflected in the x-axis to P'(5, -2). Write down the values of a and b.

(ii) P'' is the image of P when reflected in the y-axis. Write down the coordinates of P''.

(iii) Name a single transformation that maps P' into P''.

(i) Since, P'(5, -2) is the image of P under reflection in the x-axis, from graph P(5, 2).

∴ The coordinates of P are (5,2), comparing with P(a, b) we get, a = 5 and b = 2.

Hence, the value of a = 5 and b = 2.

(ii) 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.

Since, P'' is image on reflection of P(5, 2) in y-axis.

Hence, the coordinates of P'' are (-5, 2).

(iii) The single transformation that maps P'(5, -2) into P''(-5, 2) is reflection in the origin.