Question

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

Answer 1

Given, x₁ = 4

           y₁ = - 3

           x₂ = 8

           y₂ = 5

Also given the point divides the line in the ratio of 3 : 2.

So, m₁ : m₂ = 3 : 2

       Applying section formula

Required point = $\bigg(\dfrac{x_{1} m_{2} + x_{2} m_{1}}{m_{1} + m_{2}} , \dfrac{y_{1} m_{2} + y_{2} m_{1}}{m_{1} + m_{2}} \bigg)$

Required point = $\bigg( \dfrac{(4\times2)+(8\times3)}{3+2} , \dfrac{(-3x2)+(5x3)}{3+2}\bigg)$

Required point = $\bigg(\dfrac{8+24}{5} , \dfrac{-6+15}{5}\bigg)$

Required point = $\bigg( \dfrac{32}{5},\dfrac{9}{5}\bigg)$

Therefore coordinates of the point which divides the line segment joining the points (4,-3) and (8,5) in the ratio 3:2 internally is ( 32 / 5 , 9 / 5 )

Answer 2

Hey...!!
HERE IS YOUR SOLUTION....!!

Let the given points be A(4,-3) & B(8,5)

Let the point be P(x,y) which divides AB in ratio 3:2

A|________3____P|_____2____|B

Finding x___

x = m1x2 + m2x1 / m1 + m2

Where ,
m1 = 3 , x2 = 8
m2 = 2 , x1 = 4

Putting values__

x = 3×8 + 2×4 / 3+2
x = 24 + 8 / 5
x = 32 / 5___

Finding y___

y = m1y2 + m2y1 / m1 + m2

Where ,
m1 = 3 , y2 = 5
m2 = 2 , y1 = -3

Putting values___

y = 3×5 + 2×(-3) / 3+2
y = 15 - 6 / 5
y = 9 / 5___

Hence,
x = 32/5 , y = 9/5

So , the required point is P(x,y)

=P(32/5,9/5)__

BE BRAINLY !

@ujjwalusri