If the point dividing internally the line seg | vedclass

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Question

(C) Using the section formula for internal division,the coordinates of the point dividing the segment joining $(x_1, y_1)$ and $(x_2, y_2)$ in the rat

Vedclass · Accepted Answer

$a = 2, b = 4$

Vedclass · Answer

(C) Using the section formula for internal division,the coordinates of the point dividing the segment joining $(x_1, y_1)$ and $(x_2, y_2)$ in the ratio $m:n$ are given by $\left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)$.Given points are $(a, b)$ and $(5, 7)$ with ratio $2:1$ and the dividing point is $(4, 6)$.For the $x$-coordinate: $\frac{2(5) + 1(a)}{2 + 1} = 4$ $\Rightarrow \frac{10 + a}{3} = 4$ $\Rightarrow 10 + a = 12$ $\Rightarrow a = 2$.For the $y$-coordinate: $\frac{2(7) + 1(b)}{2 + 1} = 6$ $\Rightarrow \frac{14 + b}{3} = 6$ $\Rightarrow 14 + b = 18$ $\Rightarrow b = 4$.Thus,$a = 2$ and $b = 4$.

If the point dividing internally the line segment joining the points $(a, b)$ and $(5, 7)$ in the ratio $2 : 1$ is $(4, 6)$,then

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