Find the coordinates of the point R on the li | vedclass

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(D) Given that $PR = \frac{3}{5} PQ$.This implies that the point $R$ divides the line segment $PQ$ in the ratio $PR : RQ = 3 : (5 - 3) = 3 : 2$.Let th

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$(\frac{4}{5}, \frac{21}{5})$

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(D) Given that $PR = \frac{3}{5} PQ$.This implies that the point $R$ divides the line segment $PQ$ in the ratio $PR : RQ = 3 : (5 - 3) = 3 : 2$.Let the coordinates of point $R$ be $(x, y)$.Using the section formula,the coordinates of a point dividing the line segment joining $(x_1, y_1)$ and $(x_2, y_2)$ in the ratio $m : n$ are given by:$x = \frac{mx_2 + nx_1}{m + n}$,$y = \frac{my_2 + ny_1}{m + n}$Here,$(x_1, y_1) = (-1, 3)$,$(x_2, y_2) = (2, 5)$,$m = 3$,and $n = 2$.$x = \frac{3(2) + 2(-1)}{3 + 2} = \frac{6 - 2}{5} = \frac{4}{5}$$y = \frac{3(5) + 2(3)}{3 + 2} = \frac{15 + 6}{5} = \frac{21}{5}$Thus,the coordinates of point $R$ are $(\frac{4}{5}, \frac{21}{5})$.

Find the coordinates of the point $R$ on the line segment joining the points $P(-1, 3)$ and $Q(2, 5)$ such that $PR = \frac{3}{5} PQ$.

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