Question

A segment with endpoints A (3, 2) and B (6, 11) is partitioned by a point C such that AC and BC form a 2:3 ratio. Find the x value for C

Answer 1

\(\bf A(3,2)\qquad B(6,11)\\ \quad \\ \quad \\

\color{blue}{\cfrac{AC}{BC}=\cfrac{ratio1}{ratio2}\implies ratio2\cdot AC=ratio1\cdot BC\quad \textit{dividing by C}\\ \quad \\
ratio2\cdot A=ratio1\cdot B}\implies 3(3,2)=2(6,11)\\ \quad \\\qquad \color{blue}{C=\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 \\
C=\left(\cfrac{(3\cdot 3)+(2\cdot 6)}{2+3}\quad ,\quad \cfrac{(3\cdot 2)+(2\cdot 11)}{2+3}\right)\)

Answer 2

Thank you!

Answer 3

yw

Answer 4

so whats the answer haha