Four of the vertices of an irregular octagon, which is symmetrical about line y = x, are A(1, -1/2), B(4, -3), C(4, 0) and D(3, 0). (a). Find the co-ordinates of the remaining vertices. (b). The octagon is reflected in the line y = 0. Find the equation of line of symmetry of the image.

(a). Since the octagon is symmetrical about the line y = x, we can find the coordinates of the remaining vertices by reflecting the given vertices across the line y = x.

The reflection of a point (a, b) across the line y = x is the point (b, a).

So, the reflection of A(1, -1/2) is A'(-1/2, 1), the reflection of B(4, -3) is B'(-3, 4), the reflection of C(4, 0) is C'(0, 4), and the reflection of D(3, 0) is D'(0, 3).

Therefore, the coordinates of the remaining vertices are A'(-1/2, 1), B'(-3, 4), C'(0, 4), and D'(0, 3).

(b). When the octagon is reflected in the line y = 0, the line of symmetry of the image will be the line y = 0 itself. This is because the reflection of a point across the line y = 0 is the point with the same x-coordinate and the opposite y-coordinate. Therefore, the line y = 0 is the line of symmetry of the image.