Question

Calculate the coordinates of R which divides the line joining A (– 3, 3) and B (2, – 7) internally in the ratio 2 : 3.

Answer 1

Answer:

Step-by-step explanation:

A = (-3,3) = ($x_{1}$,$y_{1}$)

B = (2,-7) = ($x_{2}$,$y_{2}$)

R = (x,y)

$m_{1}$ = 2

$m_{2}$ = 3

x = $m_{1}$$x_{2}$ + $m_{2}$$x_{1}$/$m_{1}$+$m_{2}$

  = 2*2 + 3*-3/2+3

  = -1

y = $m_{1}$$y_{2}$ + $m_{2}$$y_{1}$/$m_{1}$+$m_{2}$

 = 2*-7 + 3*3/2+3

 = -1

R = (-1,-1)

Answer 2

Solution :

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Section Formula :

The coordinates of the point R(x,y)

which divides the line segment

joining the points A(x1,y1) , B(x2,y2)

internally in the ratio m1 : m2 are

x = ( m1x2 + m2x1 )/( m1 + m2 ) ,

y = ( m1y2 + m2y1 )/( m1 + m2 )

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Here ,

A( x1 , y1 ) = ( -3 , 3 ),

B( x2 , y2 ) = ( 2 , -7 ),

m1 : m2 = 2 : 3

Let R = ( x , y ) ,

x = [ 2×2+3(-3) ]/( 2 + 3 )

= ( 4 - 9 )/5

= -5/5

= -1

y = [ 2×(-7)+3(3) ]/( 2 + 3 )

= ( -14 + 9 )/5

= -5/5

= -1

Therefore ,

R( x , y ) = ( -1 , -1 )

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