Let the coordinate A be (0, c)

Equations of the given lines are

x $$-$$ y + 2 = 0 and 7x $$-$$ y + 3 = 0

We know that the diagonals of the rhombus will be parallel to the angle bisectors of the two given lines; y = x + 2 and y = 7x + 3

$$\therefore\,\,\,$$ equation of angle bisectors is given as :

$${{x - y + 2} \over {\sqrt 2 }} = \pm {{7x - y + 3} \over {5\sqrt 2 }}$$

5x $$-$$ 5y + 10 = $$ \pm $$ (7x $$-$$ y + 3)

$$\therefore\,\,\,$$ Parallel equations of the diagonals are 2x + 4y $$-$$ 7 = 0

and 12x $$-$$ 6y + 13 = 0

$$\therefore\,\,\,$$ slopes of diagonals are $${{ - 1} \over 2}$$ and 2.

Now, slope of the diagonal from A(0, c) and passing through P(1, 2) is (2 $$-$$ c)

$$\therefore\,\,\,$$ 2 $$-$$ c = 2 $$ \Rightarrow $$ c = 0 (not possible)

$$ \therefore $$$$\,\,\,$$ 2 $$-$$ c = $${{ - 1} \over 2}$$ $$ \Rightarrow $$ c = $${5 \over 2}$$

$$\therefore\,\,\,$$ Coordinate of A is $${5 \over 2}$$.