In each of the following examples find the co-ordinates of point A which divides segment PQ in the ratio a:b.

(1) Let the co-ordinates of A be (x, y).
P(-3, 7) and Q(1, -4) are the given points.
x₁ = -3 , y₁ = 7 , x₂ = 1 , y₂ = -4 , m = 2 and n = 1
By Section formula x = (mx₂+nx₁)/(m+n)
x = (2×1+1×-3)/(2+1)
x = -1/3
By Section formula y = (my₂+ny₁)/(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.
x₁ = -2 , y₁ = -5 , x₂ = 4 , y₂ = 3 , m = 3 and n = 4
By Section formula x = (mx₂+nx₁)/(m+n)
x = (3×4+4×-2)/(3+4)
x = (12+-8)/(3+4)
x = 4/7
By Section formula y = (my₂+ny₁)/(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.
x₁ = 2 , y₁ = 6 , x₂ = -4, y₂ = 1 , m =1 and n = 2
By section formula x = (mx₂+nx₁)/(m+n)
x = (1×-4+2×2)/(1+2)
x = (-4+4)/(1+2)
x = 0
By Section formula y = (my₂+ny₁)/(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)