Find the ratio in which the point P(-2, 3) di | vedclass

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(D) Let the point $P(-2, 3)$ divide the line segment $\overline{AB}$ in the ratio $m:n$ starting from $A$.Using the section formula for the $x$-coordi

Vedclass · Accepted Answer

$6$

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(D) Let the point $P(-2, 3)$ divide the line segment $\overline{AB}$ in the ratio $m:n$ starting from $A$.Using the section formula for the $x$-coordinate:$x = \frac{mx_2 + nx_1}{m + n}$Given $A(4, -9)$ as $(x_1, y_1)$ and $B(-3, 5)$ as $(x_2, y_2)$,and $P(-2, 3)$ as $(x, y)$:$-2 = \frac{m(-3) + n(4)}{m + n}$$-2(m + n) = -3m + 4n$$-2m - 2n = -3m + 4n$$-2m + 3m = 4n + 2n$$m = 6n$$\frac{m}{n} = \frac{6}{1}$Therefore,the required ratio is $6: 1$.

Find the ratio in which the point $P(-2, 3)$ divides the line segment joining $A(4, -9)$ and $B(-3, 5)$ starting from $A$. (in $: 1$)

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