See Fig. Let ABCD be the rhombus where A = (0, k). AB and CD are parallel to y + 7x + 2 whereas BC and AD are parallel to y = 2x + 3. Hence, the equation of AB is\
y = 7x + k ...(1)
Since (1, 2) is the midpoint of AC and A = (0, k), it follows that C = (2, 4 − k). Also, BC is parallel to 2x + 3 and passes through C (2, 4 − k). Hence, the equation of BC is
y -(4 - k) = 2(x - 2)
y = 2x - k ...(2)
Solving Eqs. (1) and (2), we have
B = (-2k/5, -9k/5)
Since A = (0,k), B = (-2k/5, - 9k/5), C = (2,4 - k) and AB = BC,we have