Question

Line segment AB has endpoints A(7, 4) and B(2, 5). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3. A) (7, 7 2 ) B) ( 9 2 , 5) C) ( 13 4 , 13 2 ) D) ( 23 4 , 17 4 )

Answer 1

(23/4, 17/4)

Explanation:

The vector from A to B is ...

... V = B - A = (2-7, 5-4) = (-5, 1)

Point P that divides AB the way you want is 1/4 of that from A:

... P = A + (1/4)×V = (7, 4) + (-5/4, 1/4)

... P = (5 3/4, 4 1/4) = (23/4, 17/4)