Question

The point P(0,3) divides the join of A(-2,1) and B(4,7) are in the ratio of​

Answer 1

Step-by-step explanation:

explanation is given in pictures

Answer 2

SOLUTION

TO DETERMINE

The point P(0,3) divides the join of A(-2,1) and B(4,7) are in the ratio of

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

Here the given points are A(-2,1) and B(4,7)

Let the point P(0,3) divides the join of A(-2,1) and B(4,7) are in the ratio of m : n

So by the given condition

$\displaystyle \sf{ \frac{mx_2+nx_1 \: }{m + n} \: = 0\: , \: \frac{my_2+ny_1 \: }{m + n} = 3 }$

$\displaystyle \sf{ \frac{4m - 2n \: }{m + n} = 0 \: \: , \: \frac{7m+n \: }{m + n} = 3 }$

Now

$\sf\dfrac{4m - 2n \: }{m + n} = 0$

$\sf \implies 4m - 2n = 0$

$\sf \implies 4m = 2n$

$\sf \implies \dfrac{m}{n} = \dfrac{1}{2}$

$\displaystyle \sf{ \implies m :n = 1 : 2 }$

FINAL ANSWER

The point P(0,3) divides the join of A(-2,1) and B(4,7) are in the ratio 1 : 2

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