(i) To find the equation of BC, calculate the slope using points B(4, 6) and C(x, y):

\(m_{BC} = \frac{y - 6}{x - 4} = \frac{1}{2}\)

The equation of line BC is:

\(y - 6 = \frac{1}{2}(x - 4)\)

For CD, since BC is perpendicular to CD, \(m_{BC} \times m_{CD} = -1\).

\(m_{CD} = -2\)

Using point D(12, 5), the equation of line CD is:

\(y - 5 = -2(x - 12)\)

(ii) To find the coordinates of C, solve the simultaneous equations:

\(2y = x + 8\)

\(y + 2x = 29\)

Substitute \(x = 2y - 8\) into the second equation:

\(y + 2(2y - 8) = 29\)

\(y + 4y - 16 = 29\)

\(5y = 45\)

\(y = 9\)

Substitute \(y = 9\) back into \(x = 2y - 8\):

\(x = 2(9) - 8 = 10\)

Thus, the coordinates of C are (10, 9).