Question

find the ratio in which the points (-2,3) devides the line segment joining the points (-3,5) and (4,-9)

Answer 1

Answer:

The ratio in which the points (-2,3) divides the line segment joining the points (-3,5) and (4,-9) is 1 : 6.

Step-by-step explanation:

Given points : ( -3 , 5 ) ; ( 4 , - 9 )

Point which divides the given points : ( - 2 , 3 )

By Section Formula, we can calculate the ratio in which the point ( - 2 , 3 ) divides the given points.

According to the section formula,

$X=\dfrac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}},Y=\dfrac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}}$ ,where x₂ and x₁ are the co ordinates of x - axis of the particular line and y₂ and y₁ are the co ordinates of y - axis of the particular line. m₁ and m₂ is the ratio in which the points ( X , Y ) divides ( x₁ , y₁ ) and ( x₂ , y₃ ).

Now, applying the section formula,

Given,

   Co ordinate on x - axis of the point which the given points is -2 .

Therefore, assume x₁ = - 3 , x₂ = 4 and m₁ & m₂ be the ratio .

So,

$\implies -2=\dfrac{ (m_{1} \times 4 )+(m_{2}\times -3) }{m_{1}+m_{2}}$

$\implies -2m_{1} -2m_{2} = 4m_{1}-3m_{2}$

= >  - 2m₁ - 4m₁ = - 3m₂ + 2m₂

= >  - 6m₁ = - m₂

= >  m₁ : m₂ = 1 : 6

Answer 2

Answer:

1:6

Step-by-step explanation:

Given points are A(-2,3), B(-3,5) and C(4,-9)

Let the ratio be k:1.

Here, (x₁,y₁) = (-3,5), (x₂,y₂) = (4,-9), (x,y) = (-2,3), (m₁,m₂) = (k,1)

Section formula:

⇒ x = (m₁x₂ + m₂x₁)/(m₁ + m₂)

⇒ -2 = (k*4 - 3)/k + 1

⇒ -2(k + 1) = 4k - 3

⇒ -2k - 2 = 4k - 3

⇒ -2k - 4k = -3 + 2

⇒ -6k = -1

⇒ k = 1/6

Hence, the ratio is k:1

⇒ 1/6 : 1

⇒ 1:6

Therefore, the ratio is 1:6.

Hope it helps!