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find the ratio in which point P(-1,y) lying on the line segment joining points A(-3,10) and B(6,-8) divides it. also find the value of y.

$L e t t h e p o int (- 1, y) d i v i d e s t h e l i n e s e g m e n t j o i n i n g p o int s A (- 3, 10) a n d B (6, - 8) i n t h e r a t i o n k : 1 T h e n, t h e c o o r d i n a t e o f p o int P = (\frac{6 k - 3}{k + 1}, \frac{- 8 k + 10}{k + 1}) (T h e c o o r d i n a t e o f t h e p o int w h i c h d i v i d e s t h e l i n e s e g m e n t j o i n i n g p o int s (x_{1}, y_{1}) a n d (x_{2}, y_{2}) int e r n a l l y i n t h e r a t i o n m : n i s (x = \frac{m x_{2} + n x_{1}}{m + n}, y = \frac{m y_{2} + n y_{1}}{m + n})) B u t, c o o r d i n a t e o f p o int P = (- 1, y) (g i v e n) T h u s, - 1 = \frac{6 k - 3}{k + 1} \Rightarrow - k - 1 = 6 k - 3 \Rightarrow 7 k = 2 \Rightarrow k = \frac{2}{7} A n d y = \frac{- 8 k + 10}{k + 1} \Rightarrow y = \frac{- 8 (\frac{2}{7}) + 10}{\frac{2}{7} + 1} \Rightarrow y = \frac{- 16 + 70}{2 + 7} \Rightarrow y = \frac{54}{9} \Rightarrow y = 6 H e n c e, t h e r a t i o i s 2 : 7 a n d y = 6$

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