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(B) Using the section formula,if a point $P(x, y)$ divides the line segment joining $A(x_1, y_1)$ and $B(x_2, y_2)$ in the ratio $m:n$,then the coordi

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$4$

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(B) Using the section formula,if a point $P(x, y)$ divides the line segment joining $A(x_1, y_1)$ and $B(x_2, y_2)$ in the ratio $m:n$,then the coordinates are given by:$x = \frac{mx_2 + nx_1}{m+n}$ and $y = \frac{my_2 + ny_1}{m+n}$Here,$A(1, 2)$,$B(4, 5)$,$m:n = 2:1$,and $P(3, b)$.To find $b$,we use the $y$-coordinate formula:$b = \frac{m(y_2) + n(y_1)}{m+n}$$b = \frac{2(5) + 1(2)}{2+1}$$b = \frac{10 + 2}{3}$$b = \frac{12}{3}$$b = 4$Therefore,the value of $b$ is $4$.

The point $P(3, b)$ divides the line segment joining $A(1, 2)$ and $B(4, 5)$ in the ratio $2:1$ from $A$. Find the value of $b$.

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