Given vertices of the triangle are A(-5,3), B(p,-1) and C(6,q).

Co-ordinates of centroid are (1,-1).

Co-ordinates of the centroid of a triangle, whose vertices are (x₁,y₁), (x₂,y₂) and (x₃,y₃) are

[(x₁ + x₂+ x₃)/3, (y₁ + y₂+ y₃)/3]

(x₁,y₁) = (-5,3)

(x₂,y₂) = (p,-1)

(x₃,y₃) = (6,q)

x co-ordinate of centroid, (x₁ + x₂+ x₃)/3 = (-5+p+6)/3 = 1

p+1 = 3

p = 3-1

p = 2

y co-ordinate of centroid, (y₁ + y₂+ y₃)/3 = (3-1+q)/3 = -1

2+q = 3×-1

2+q = -3

q = -3-2

q = -5

Hence the value of p and q are 2 and -5 respectively.