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Mathematics

Find the coordinates of the point which divides the join of (-1, 7) and (4, -3) in the ratio 2 : 3.

Coordinate Geometry

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Answer

By section-formula,

(x, y) = (m1x2+m2x1m1+m2,m1y2+m2y1m1+m2)\Big(\dfrac{m1x2 + m2x1}{m1 + m2}, \dfrac{m1y2 + m2y1}{m1 + m2}\Big)

Let (x, y) divide the join of (-1, 7) and (4, -3) in the ratio 2 : 3.

Substituting values we get :

(x,y)=(2×4+3×12+3,2×3+3×72+3)=(8+(3)5,6+215)=(55,155)=(1,3).\Rightarrow (x, y) = \Big(\dfrac{2 \times 4 + 3 \times -1}{2 + 3}, \dfrac{2 \times -3 + 3 \times 7}{2 + 3}\Big) \\[1em] = \Big(\dfrac{8 + (-3)}{5}, \dfrac{-6 + 21}{5}\Big) \\[1em] = \Big(\dfrac{5}{5}, \dfrac{15}{5}\Big) \\[1em] = (1, 3).

Hence, point (1, 3) divides the join of (-1, 7) and (4, -3) in the ratio 2 : 3.

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