Given A(2,3) and B(7,-4), find the coordinates of P such that AP/PB = 2/5.

Question

Hi! Please clearly write out and explain how I am meant to answer this, it would be greatly appreciated.

Also please use the “Division of an interval in a given ratio” if possible :)

Answer 1

2+5 = 7.  So, we are trying to find point P such that P is 2/7 of the way along line segment AB from A to B.

 

As we move along AB from A to B, x increases by 5 and y decreases by 7.

 

x-coordinate of P:  2 + (2/7)(5) = 24/7

 

y-coordinate of P:  3 - (2/7)(7) = 1

 

P = (24/7, 1)