The endpoints of MP are M(1,4) amd P(16,14). If A partitions MP in a ratio of MA:AP = 2:1, which of the following represent the coordinates of point A?
Accepted Solution
A:
so, we know the segment MP gets partitioned by the point A to MA with a ratio of 2 and AP with a ratio of 1, on a 2:1 ratio from M to P, therefore then,
[tex]\bf \left. \qquad \right.\textit{internal division of a line segment}
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M(1,4)\qquad P(16,14)\qquad
\qquad 2:1
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\cfrac{MA}{AP} = \cfrac{2}{1}\implies \cfrac{M}{P} = \cfrac{2}{1}\implies 1M=2P\implies 1(1,4)=2(16,14)\\\\
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{ A=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}[/tex]