Question

A segment with endpoints A (2, 6) and C (5, 9) is partitioned by a point B such that AB and BC form a 3:1 ratio. Find B.

(2.33, 6.33)
(3.5, 10.5)
(3.66, 7.66)
(4.25, 8.25)

Answer 1

@whpalmer4

Answer 2

@AccessDenied

Answer 3

@Hero

Answer 4

\(\bf\color{blue}{ A(2,6)\qquad C(5,9)\qquad ratio1=3\qquad ratio2=1\qquad 3:1}\\ \quad \\ \quad \\

\cfrac{AB}{CB}=\cfrac{ratio1}{ratio2}\implies ratio2\cdot AB=ratio1\cdot CB\quad \textit{dividing by B}\\ \quad \\
ratio2\cdot A=ratio1\cdot C\implies 1(2,6)=3(5,9)\\ \quad \\\qquad \color{blue}{B=\left(\cfrac{\textit{sum of "x" values}}{ratio1+ratio2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{ratio1+ratio2}\right)}\\ \quad \\

\qquad thus\qquad \\ \quad \\
B=\left(\cfrac{(1\cdot 2)+(3\cdot 5)}{3+1}\quad ,\quad \cfrac{(1\cdot 6)+(3\cdot 9)}{3+1}\right)\)

Answer 5

Thanks a lot and great explanation!

Answer 6

yw