(1) Let the co-ordinates of A be (x, y).

P(-3, 7) and Q(1, -4) are the given points.

x_{1} = -3 , y_{1} = 7 , x_{2} = 1 , y_{2} = -4 , m = 2 and n = 1

By Section formula x = (mx_{2}+nx_{1})/(m+n)

x = (2×1+1×-3)/(2+1)

x = -1/3

By Section formula y = (my_{2}+ny_{1})/(m+n)

y = (2×-4+1×7)/3

y = (-8+7)/3

y = -1/3

Hence the co-ordinates of A is (-1/3 , -1/3)

(2) Let the co-ordinates of A be (x, y).

P(-2, -5), and Q(4, 3), are the given points.

x_{1} = -2 , y_{1} = -5 , x_{2} = 4 , y_{2} = 3 , m = 3 and n = 4

By Section formula x = (mx_{2}+nx_{1})/(m+n)

x = (3×4+4×-2)/(3+4)

x = (12+-8)/(3+4)

x = 4/7

By Section formula y = (my_{2}+ny_{1})/(m+n)

y = (3×3+4×-5)/(3+4)

y = (9-20)/7

y = -11/7

Hence the co-ordinates of A is (4/7 , -11/7)

(3) Let the co-ordinates of A be (x, y).

P(2, 6), and Q(-4, 1), are the given points.

x_{1} = 2 , y_{1} = 6 , x_{2} = -4, y_{2} = 1 , m =1 and n = 2

By section formula x = (mx_{2}+nx_{1})/(m+n)

x = (1×-4+2×2)/(1+2)

x = (-4+4)/(1+2)

x = 0

By Section formula y = (my_{2}+ny_{1})/(m+n)

y = (1×1+2×6)/(1+2)

y = (1+12)/3

y = 13/3

Hence the co-ordinates of A is (0 , 13/3)