Point C(4,2) divides the line segment joining points A(2,-1) and B(x,y) such that AC:BC =3:1what are the coordinates of point B

Answer 1

A(2,-1) C(4,2) B(x,y)

3:1 = AC:BC

4-2 = 2, 2:2/3 = 3:1 x= 4 2/3

2--1 = 3, 3:1 add 1 to 2=3 = y

B(x,y) = B(4 2/3, 3)

distance AC = sqr(4+9) = sqr13

distance BC = sqr(4/9+1) = sqr13/9= (1/3)sqr13

sqr13 = 3 times (1/3)sqr13, it's a 3:1 ratio

AC = sqr(2^2 + 3^2) = sqr13