Given, ABCD is a rhombus and co-ordinates of A are (3, 6) and of C are (-1, 2)

Slope of AC (m₁) = (2 – 6)/ (-1 – 3) = -4/-4 = 1

We know that, the diagonals of a rhombus bisect each other at right angles.

So, the diagonal BD is perpendicular to diagonal AC

Let the slope of BD be m₂

Then, m₁ x m₂ = -1

m₂ = -1/(m₁)

= -1/ (1) = -1

Now, the co-ordinates of the mid-point of AC is given by

((3 – 1)/2, (6 + 2)/2) = (2/2, 8/2) = (1, 4)

So, the equation of BD will be

y – 4 = -1 (x – 1)

y – 4 = -x + 1

x + y = 5

Thus, the equation of BD is x + y = 5.