Given, points B (1, 3) and D (6, 8) are two opposite vertices of a square ABCD

Slope of BD is given by

m₁ = (8 – 3)/ (6 – 1) = 5/5 = 1

We know that, the diagonal AC is a perpendicular bisector of diagonal BD

So, the slope of AC (m₂) will be

m₁ x m₂ = -1

1 x m₂ = -1

m₂ = -1

And, the co-ordinates of mid-point of BD and AC will be

((1 + 6)/2 , (3 + 8)/2) = (7/2, 11/2)

So, the equation of AC is

y – 11/2 = -1 (x – 7/2)

2y – 11 = -2x – 7

2x + 2y – 7 – 11 = 0 ⇒ 2x + 2y – 18 = 0

Thus, the equation of diagonal AC is x + y – 9 = 0.