Respuesta :
let's say that point is point C, thus
[tex]\bf ~~~~~~~~~~~~\textit{internal division of a line segment}\\\\\\A(1,4)\qquad B(6,2)\qquad\qquad \stackrel{\textit{ratio from A to B}}{2:3}\\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(1,4)=2(6,2)\\\\[-0.35em]~\dotfill\\\\C=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em]~\dotfill[/tex]
[tex]\bf C=\left(\cfrac{(3\cdot 1)+(2\cdot 6)}{2+3}\quad ,\quad \cfrac{(3\cdot 4)+(2\cdot 2)}{2+3}\right)\implies C=\left(\cfrac{3+12}{5}~,~\cfrac{12+4}{5} \right)\\\\\\C=\left( \cfrac{15}{5}~,~\cfrac{16}{5} \right)\implies C=\left( 3~,~3\frac{1}{5} \right)[/tex]
Answer:
D. ( 24/5, 19/5)
Step-by-step explanation:
(mx2 + nx1) (my2 + ny1)
(m + n) , (m + n)
Where the point divides the segment internally in the ratio m:n
((2)(3) + (3)(6)) ((2)(8) + (3)(1))
(2 + 3) , (2 + 3) = 24/5, 19/5
