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Section Formula

The point 19,...

Question

The point (19,-23) divides the line joining points J(4, -5), L(-6, 7)in ratio $=$ 3:5.
If true then enter $1$ and if false then enter $0$

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Solution

$L e t t h e c o - o r d i n a t e s o f t h e p o i n t P b e P (x, y) w h i c h d i v i d e s t h e l i n e s e g m e n t J L j o i n i n g t h e p o i n t s J (x_{1}, y_{1}) = (4, - 5) & L (x_{2}, y_{2}) = (- 6, 7) i n t h e r a t i o m : n = 3 : 5. T h e n, b y t h e s e c t i o n f o r m u l a, x = \frac{n x_{1} - m x_{2}}{n - m} = \frac{5 \times 4 - 3 \times (- 6)}{5 - 3} = 19 a n d y = \frac{n y_{1} - m y_{2}}{n - m} = \frac{5 \times (- 5) - 3 \times 7}{5 - 3} = - 23 ∴ P (x, y) = P (19, - 23) . A n s - P (x, y) = P (- \frac{6}{7}, 2) .$

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