Find the points of trisection of the line seg | vedclass

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(C) Let the points of trisection be $P_1$ and $P_2$. $P_1$ divides $AB$ in the ratio $1:2$ and $P_2$ divides $AB$ in the ratio $2:1$.Using the section

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$\left( 3, \frac{5}{3} \right), \left( 4, \frac{7}{3} \right)$

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(C) Let the points of trisection be $P_1$ and $P_2$. $P_1$ divides $AB$ in the ratio $1:2$ and $P_2$ divides $AB$ in the ratio $2:1$.Using the section formula $\left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)$:For $P_1$ (ratio $1:2$): $x = \frac{1(5) + 2(2)}{1+2} = \frac{9}{3} = 3$,$y = \frac{1(3) + 2(1)}{1+2} = \frac{5}{3}$. So,$P_1 = \left( 3, \frac{5}{3} \right)$.For $P_2$ (ratio $2:1$): $x = \frac{2(5) + 1(2)}{2+1} = \frac{12}{3} = 4$,$y = \frac{2(3) + 1(1)}{2+1} = \frac{7}{3}$. So,$P_2 = \left( 4, \frac{7}{3} \right)$.

Find the points of trisection of the line segment joining the points $A(2, 1)$ and $B(5, 3)$.

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