In a ΔABC, ∠A = 90° and the coordinate of A is (2, 1) and the mid-point of the hypotenuse is $\left(\frac{3}{2}, \frac{-5}{2}\right)$. If the coordinate of its centroid is G(p, q), then the value of p – q is

The point which is common to all the three medians is called the centroid and this point divides each median in the ratio 2:1.
Now, apply the section formula
m₁=2
m₂=1
x₁ = 2      y₁ = 1
x₂  = 32  y₂ = 52  

You will get (p,q)=(22,35)
p=22      q=35

p-q
=22-35
= -12.