Question

Find the ratio in which the line segment joining the points (6, 4) and (1, -7) is divided internally by the axis X​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

The ratio in which the line segment joining the points (6, 4) and (1, -7) is divided internally by the x axis

FORMULA TO BE IMPLEMENTED

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

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

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

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

CALCULATION

Let m : n be the ratio in which the line segment joining the points (6, 4) and (1, -7) is divided internally by the x axis

The coordinate of point where it is divided is

$= \displaystyle \sf{ \bigg( \frac{m+6n \: }{m + n} \: \: , \: \frac{ - 7m+4n \: }{m + n} \bigg) }$

Since the point is on x axis

So

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

$\implies \sf{ - 7m + 4n = 0}$

$\implies \sf{ 7m = 4n }$

$\implies \displaystyle \sf{ \frac{m}{n} = \frac{4}{7} }$

$\implies \displaystyle \sf{ m : n = 4 :7 }$

RESULT

Hence the required ratio is 4 : 7

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