The point P(2, -7) is reflected in the point (0, 3); the co-ordinates of the image of point P are :

1. (2, 13)

2. (2, -13)

3. (-2, -13)

4. (-2, 13)

Let point P on reflection in the point (0, 3) becomes P'(x, y).

So, (0, 3) will be the mid-point of PP'.

By formula,

Mid-point = $\Big(\dfrac{x$1 + x2}{2}, \dfrac{y1 + y2}{2}\Big)

Substituting values we get :

$\Rightarrow (0, 3) = \Big(\dfrac{2 + x}{2}, \dfrac{-7 + y}{2}\Big) \\[1em] \Rightarrow 0 = \dfrac{2 + x}{2} \text{ and } 3 = \dfrac{-7 + y}{2} \\[1em] \Rightarrow 2 + x = 0 \text{ and } -7 + y = 6 \\[1em] \Rightarrow x = -2 \text{ and } y = 6 + 7 \\[1em] \Rightarrow x = -2 \text{ and } y = 13.$

P' = (-2, 13).

Hence, Option 4 is the correct option.