Question

(2, - 3) ಮತ್ತು (5, 6) ಬಿಂದುಗಳನ್ನು ಸೇರಿಸುವ ರೇಖೆಯನ್ನು Yಅಶ್ವವು ಯಾವ ಅನುಪಾತದಲ್ಲಿ ವಿಭಾಗಿಸುತ್ತದೆ ಕಂಡುಹಿಡಿಯಿರಿ .​

Answer 1

SOLUTION

TO DETERMINE

The ratio by which the line joining the points (2, - 3) and (5, 6) cuts by y axis

CONCEPT TO BE IMPLEMENTED

$\sf{The \: coordinate \: of \: the \: point \: where \: the \: line }$

$\sf{joining \: the \: points \: (x_1,y_1) \: and \: (x_2,y_2) \: in }$

$\sf{the \: ratio \: \: m :n \: \: is }$

$= \displaystyle \sf{ \bigg( \frac{mx_2+nx_1 \: }{m + n} \: \: , \: \frac{my_2+ny_1 \: }{m + n} \bigg) }$

EVALUATION

Let the required ratio = m : n

Now the given points are (2, - 3) and (5, 6)

Now the point where the line joining the points (2, - 3) and (5, 6) in the ratio m : n is

$\displaystyle\sf{ = \bigg( \frac{5m+2n \: }{m + n} \: \: , \: \frac{6m - 3n \: }{m + n} \bigg) }$

Now the point lies on y axis

So Abscissa of the point = 0

$\displaystyle\sf{ \implies \: \frac{5m+2n \: }{m + n} = 0 }$

$\displaystyle\sf{ \implies \: 5m+2n = 0 }$

$\displaystyle\sf{ \implies \: 5m = - 2n }$

$\displaystyle\sf{ \implies \: \frac{m}{n} = - \frac{2}{5} }$

FINAL ANSWER

The line joining the points (2, - 3) and (5, 6) cuts by y axis externally in the ratio 2 : 5

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Answer 2

Step-by-step explanation:

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