Question

The point which divides the line segment joining the points (7.-6) and (3.4) in the ratio 1:2 lies in the​

Answer 1

Given :-

The point which divides the line segment joining the points (7.-6) and (3.4) in the ratio 1:2

To Find :-

In which quadrant it lies

Solution :-

By using section formula

$\sf P(x,y) = \bigg(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\bigg)$

Where

m = 1

n = 2

x₁ = 7

x₂ = 3

y₁ = -6

y₂ = 4

P(x,y) = [1(3) + 2(7)/1 + 2 , 1(4) + 2(-6)/1 + 2]

= [3 + 14/3, 4 + (-12)/3]

= 17/3, 4 - 12/3

= 17/3, -8/3

As the x coordiante is positive and y coordinate is negaticve. Therefore, it lies in 4th quadrant

Answer 2

$\textbf{\huge{\green{Solution}} }$

The point which divides the line segment joining the points (7.-6) and (3.4) in the ratio 1:2 lies in the ?

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$\large\ \ \ \ \ \orange{\underline{\underline{To\:find:}}}$

In which quadrant it lies

$\large\ \ \ \ \ \red{\underline{\underline{Solution}}}$

By using section formula ,

P( x , y ) = ($\dfrac{mx2 + nx1}{m + n}$ , $\dfrac{my2 + ny1}{m +n}$)

Where ,

ㅤㅤㅤㅤm = 1

ㅤㅤㅤㅤn = 2

ㅤㅤㅤㅤx1 = 7

ㅤㅤㅤㅤx2 = 3

ㅤㅤㅤㅤy = -6

ㅤㅤㅤㅤy2 = 4

P( x , y ) = $(1(3)+\dfrac{2(7)}{1}+2 , 1(4) + \dfrac{2(-6)}{1}+3)$

$\implies$ $( 3 + \dfrac{14}{3} , 4 + \dfrac{(-12)}{3} )$

$\implies$ $\dfrac{17}{3} , 4 - \dfrac{12}{3}$

$\implies$ $\dfrac{17}{3} , \dfrac{-8}{3}$

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As the x coordinate is positive & y coordinate is negative . Therefore , it lies in 4th quadrant.