(C) Let the points be $A(-3, 2)$ and $B(3, -4)$. The ratio is $m : n = 3 : 2$. Using the section formula,the coordinates of the point $R(x, y)$ are gi

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$\left( \frac{3}{5}, - \frac{8}{5} \right)$

(C) Let the points be $A(-3, 2)$ and $B(3, -4)$. The ratio is $m : n = 3 : 2$. Using the section formula,the coordinates of the point $R(x, y)$ are given by: $x = \frac{mx_2 + nx_1}{m + n} = \frac{3(3) + 2(-3)}{3 + 2} = \frac{9 - 6}{5} = \frac{3}{5}$ $y = \frac{my_2 + ny_1}{m + n} = \frac{3(-4) + 2(2)}{3 + 2} = \frac{-12 + 4}{5} = -\frac{8}{5}$ Thus,the coordinates of the point are $\left( \frac{3}{5}, - \frac{8}{5} \right)$.

Class 11 Mathematics Straight Line System of co-ordinates, Distance between two points, Section formulae

Easy

Find the coordinates of the point that divides the line segment joining the points $(-3, 2)$ and $(3, -4)$ internally in the ratio $3 : 2$.

A
$(2, 3)$
B
$\left( \frac{2}{5}, - \frac{4}{3} \right)$
C
$\left( \frac{3}{5}, - \frac{8}{5} \right)$
D
$(0, 4)$

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System of co-ordinates, Distance between two points, Section formulae

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Find the coordinates of the point that divides the line segment joining the points $(-3, 2)$ and $(3, -4)$ internally in the ratio $3 : 2$.

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