The point P(m, n) is first reflected in x-axis to point P' and then point P' is reflected in y-axis to point P". Then the single transformation that reflects point P to P" is :

1. reflection in x-axis

2. reflection in y-axis

3. reflection in origin

4. invariant

We know that,

On reflection in x-axis, the sign of y-coordinate changes.

So,

P(m, n) ⇒ P'(m, -n)

On reflection in y-axis, the sign of x-coordinate changes.

So,

P'(m, -n) ⇒ P"(-m, -n)

We know that,

On reflection in origin, the sign of both the coordinate changes.

P(m, n) ⇒ P"(-m, -n)

∴ The single transformation that reflects point P to P" is reflection in origin.

Hence, Option 3 is the correct option.