Respuesta :

[tex]\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ A(-6,3)\qquad B(8,10)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:4} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{3}{4}\implies \cfrac{A}{B} = \cfrac{3}{4}\implies 4A=3B\implies 4(-6,3)=3(8,10)\\\\[-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{(4\cdot -6)+(3\cdot 8)}{3+4}\quad ,\quad \cfrac{(4\cdot 3)+(3\cdot 10)}{w+z}\right) \\\\\\ C=\left(\cfrac{(-24)+(24)}{7}\quad ,\quad \cfrac{(12)+(30)}{7}\right)\implies C=\left( \cfrac{0}{7}~,~\cfrac{42}{7} \right)\implies C=(0,6)[/tex]

varshamittal029

the coordinate of the point that diivides the line segment in 3:4 is (0,6).

What is section fomula?

if a poInt divides the line segment joining two point (x₁,y₁) and (x₂,y₂) in ratio m:n, which is internal division of the two point the coordinate of that point is (mx₂+nx₁/m+n , my₂+ny₁/m+n)

According to the asked question,

x₁=-6,y₁=3

x₂=8,y₂=10

m=3

n=4

so using the above section formula the coordinate of the point which divides the line segment into 3:4 is

=(mx₂+nx₁/m+n , my₂+ny₁/m+n)

=(3*8+4(-6)/3+4,3*10+4*3/3+4)

=(0/7,42/7)

=(0,6)

Therefore, the coordinate of the point that diivides the line segment in 3:4 is (0,6).

Learn more about section formula

here: https://brainly.com/question/7041827

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