Question

Points A, P and B are collinear such that P sits on line segment AB and partitions the segment so that AP to PB is in the ratio 2:3. Point A is located at (3,-1) and B is located at (8,14). Find the coordinates of P, the partition point.

Answer 1

P = (5, 5)

Explanation:

For the given division, ...

P = (2B +3A)/5

P = (2(8, 14) +3(3, -1))/5 = (16+9, 28-3)/5 = (25, 25)/5

P = (5, 5)

_____

For some division ratio of AP : PB = p : q, we have ...

(P -A)/(B -P) = p/q

q(P -A) = p(B -P)

P(p+q) = pB +qA . . . . rearranging

P = (pB +qA)/(p+q) . . . . . the formula we used above