Question

Find the coordinates of the point which divides the line segment joining the points (4, – 3) and (8,5) in the ratio 2:1 internally.

Please Help​

Answer 1

Let the point be M(x,y)

A/q ,

(x,y) =[ {( 2 . 8 + 1 . 4)/ 2+1 } , {(2 . 5 + 1 . (-3) )/2+1 }]

= (20/3 , 7 /3 )

Answer 2

Answer:

The formula to find the coordinates of Point of Division, when line is divided internally, is given as:

$\boxed{ \bf{ (x, y) = [\dfrac{ mx_2 + nx_1}{m+n}\:,\: \dfrac{my_2 + ny_1}{m+n}]}}$

According to the question,

• x₁ = 4, y₁ = -3
• x₂ = 8, y₂ = 5
• m : n =  ( 2 : 1 )

Substituting the values we get:

$\implies x-coordinate = \dfrac{ mx_2 + nx_1}{m+n}\\\\\\\implies x= \dfrac{ 2(8) + 1(4)}{2+1}\\\\\\\implies \boxed{ \bf{ x = \dfrac{20}{3}}}$

Similarly,

$\implies y-coordinate = \dfrac{my_2 + ny_1}{m+n}\\\\\\\implies y = \dfrac{ 2(5) + 1(-3) }{2 + 1 }\\\\\\\implies \boxed{ \bf{ y = \dfrac{7}{3}}}$

Hence the coordinate where the line is divided internally is: ( 20/3, 7/3 )