Question

Consider A = (-9,4) and B (11,17). = Point P₂ partitions the segment from B to A in a 3:5 ratio. Find the coordinates of point P2.

Answer 1

An easy way to do this is to parameterize the directed line segment from B to A by the function

$\ell_{B\to A}(t) = (1-t) B + t A = (1 - t) (11, 17) + t (-9, 4)$

with 0 ≤ t ≤ 1.

The point P₂ splits up AB so that BP₂ = 3/8 AB and AP₂ = 5/8 AB. Then we reach the point P₂ when t = 3/8, so its coordinates are

$P_2 = \ell_{B\to A}}\left(\dfrac38\right) = \dfrac58 (11,17) + \dfrac38 (-9,4) = \boxed{\left(\dfrac72, \dfrac{97}8\right)}$