2 years ago

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Mathematics

1 answer:

vlabodo [156]2 years ago

7 0

Answer: 108

Step-by-step explanation:

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Find point P that divides segments AB into a 2:3 ratio.

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$\bf ~~~~~~~~~~~~\textit{internal division of a line segment}
\\\\\\
A(-3,1)\qquad B(3,5)\qquad
\qquad \stackrel{\textit{ratio from A to B}}{2:3}
\\\\\\
\cfrac{A\underline{P}}{\underline{P} B} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(-3,1)=2(3,5)\\\\
-------------------------------\\\\
P=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)$

$\bf -------------------------------\\\\
P=\left(\cfrac{(3\cdot -3)+(2\cdot 3)}{2+3}\quad ,\quad \cfrac{(3\cdot 1)+(2\cdot 5)}{2+3}\right)
\\\\\\
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Which order does it go?

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