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

As given the coordinates of A(−2, −2) and B(2, −4) and P is a point lies on AB. And AP = (3/7)AB ∴ BP = (4/7)AB
Then, ratio of AP and PB = m1:m2 = 3:4
Let the coordinates of P be (x, y).
∴ x = (m1x2 + m2x1) / (m1 + m2) ⇒ x = (3 × 2 + 4 × (−2)) / (3 + 4) = (6 − 8) / 7 = −2/7
And y = (m1y2 + m2y1) / (m1 + m2) ⇒ y = (3 × (−4) + 4 × (−2)) / (3 + 4) = (−12 − 8) / 7 = −20/7
∴ Coordinates of P = (−2/7, −20/7)