Find the coordinates of the point which divid | vedclass

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Question

(A) Let $P(x, y)$ be the required point that divides the line segment joining $A(4, -3)$ and $B(8, 5)$ in the ratio $m:n = 3:1$.Using the section form

Vedclass · Accepted Answer

($7$,$3$)

Vedclass · Answer

(A) Let $P(x, y)$ be the required point that divides the line segment joining $A(4, -3)$ and $B(8, 5)$ in the ratio $m:n = 3:1$.Using the section formula,the coordinates $(x, y)$ are given by:$x = \frac{mx_2 + nx_1}{m + n} = \frac{3(8) + 1(4)}{3 + 1} = \frac{24 + 4}{4} = \frac{28}{4} = 7$$y = \frac{my_2 + ny_1}{m + n} = \frac{3(5) + 1(-3)}{3 + 1} = \frac{15 - 3}{4} = \frac{12}{4} = 3$Therefore,the required point is $(7, 3)$.

Find the coordinates of the point which divides the line segment joining the points $(4, -3)$ and $(8, 5)$ in the ratio $3: 1$ internally.

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