UPSKILL MATH PLUS
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Learn moreLet us look at the graph carefully.
From the graph, the line \(AB\) is divided at \(P\) in the ratio \(m : n\).
Therefore, \(\frac{AP}{AB} = \frac{m}{n}\).
So, \(A'P' : P'B'\) is also \(m : n\).
\(\frac{A'P'}{A'B'} = \frac{m}{n}\)
\(n(A'P') =\) \(m(A'B')\)
\(n(x - x_1) =\) \(m(x_2 - x)\)
\(nx - nx_1 = mx_2 - mx\)
\(mx + nx = mx_2 + nx_1\)
\(x\) \(=\) \(\frac{mx_2 + nx_1}{m + n}\)
Similarly, \(y\) \(=\) \(\frac{my_2 + ny_1}{m + n}\).
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