If the coordinates of points A and B are (−2, −2) and (2, −4) respectively, find the coordinates of P such that AP = (3/7)AB, where P lies on the line segment AB.

Given coordinates of point A(−2, −2) and B(2, −4) and point P divided AB as AP = (3/7)AB
Then BP = (4/7)AB
So point P divided AB in ratio 3:4
m = 3 and n = 4
Using Section formula, coordinates of point P are
[x = (mx₁ + nx₂)/(m + n)] and [y = (my₁ + ny₂)/(m + n)]
A(−2, −2) ≡ (x₂, y₂) and B(2, −4) ≡ (x₁, y₁)
P = (3 × 2 − 2 × 4)/(3 + 4), (−4 × 3 + 2 × 4)/(3 + 4) = (6 − 8)/7, (−12 + 8)/7 = (−2/7, −4/7)