Based on the sequence of transformations, the coordinates of P" are P" (-5, -1).
In Mathematics and Euclidean Geometry, a reflection over the line x = n can be represented by the following transformation rule (x, y) → (2n - x ,y);
(x, y) → (-4 - x ,y)
By applying a reflection over the line x = -2 to the coordinates of point P (1, 3), we have the following coordinates of its image;
(x, y) → (-4 - x', y')
P (1, 3) → (-4 - 1, 3) = P' (-5, 3)
Next, we would apply a translation 4 units down to the new point based on the given transformation rule, in order to determine the coordinates of its image as follows;
(x, y) → (x', y' - 4)
P (-5, 3) → (-5, 3 - 4) = P" (-5, -1)