Question

6. Find the coordinates of the point which divides the line segment joining (3, 4) and
(–6, 2) in the ratio 3 : 2 externally.

Answer 1

Let the point P which divides the line segment joining (3,4) and (-6,2) in the ratio 3 :2 externally.

we have , if two point (x₁ ,y₁) and (x₂, y₂) are divided by P(x, y) in the ratio m : n.
Then, x = (mx₂ - nx₁)/(m - n) and y = (my₂ - ny₁)/(m - n)

Here, (x₁ , y₁) = (3,4)
(x₂ , y₂) = (-6,2)
m : n = 3 : 2
Now, x = (3 × -6 - 2 × 3)/(3 - 2) = (-18 - 6)/1 = -24
y = (3 × 2 - 2 × 4)/(3 - 2) = (6 - 8)/1 = -2
Hence, P ≡( -24 , -2)

Answer 2

Solution :

__________________________

The coordinates of the points which

divides the line joining ( x1 , y1 ) and

( x2, y2 ) in the ratio of m : n externally

is ( x , y ) ,

x = (mx2 - nx1 )/( m - n ),

y = ( my2 - ny1 )/( m -n )

____________________________

Given ( x1 , y1 ) = ( 3 , 4 ) ,

( x2 , y2 ) = ( -6 , 2 ) ,

m : n = 3 : 2

Now ,

x = ( 3 × -6 - 2 × 3 )/( 3 - 2 )

= ( -18 - 6 )

= -24

x = -6

y = ( 3 × 2 - 2 × 4 )/( 3 -2 )

= ( 6 - 8 )

= -2

y = -2

∴ Required point = ( x , y ) = ( -24 , -2)

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