Point A is located at (5, 10) and point B is located at (20, 25).What point partitions the directed line segment AB¯¯¯¯¯ into a 3:7 ratio?
Accepted Solution
A:
let's say the point is C, so C partitions AB into two pieces, where AC is at a ratio of 3 and CB is at a ratio of 7, thus 3:7,
[tex]\bf \left. \qquad \right.\textit{internal division of a line segment}
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A(5,10)\qquad B(20,25)\qquad
\qquad 3:7
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\cfrac{AC}{CB} = \cfrac{3}{7}\implies \cfrac{A}{B} = \cfrac{3}{7}\implies 7A=3B\implies 7(5,10)=3(20,25)\\\\
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{ C=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}\\\
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