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

Question

Philoid · Accepted Answer

Let the point P(x,y) divides AB

Then

X = (m₁x₂ + m₂x₁)/ m₁ + m₂

= (3 × 2) + 4x (– 2))/ 3 + 4

= (6 – 8)/7

= – 2/7

Y = (m₁y₂ + m₂y₁)/ m₁ + m₂

= (3 × (– 4) + 4 × (– 2))/ 7

= (– 12 – 8)/ 7

= – 20 / 7