Math, asked by SHREYASHJADHAV10, 2 months ago

What ratio the line joining - 1,1 and 5,7 is divided by the line X + y is equal to 4​

Answers

Answered by Anonymous
4

Answer:

  • Ratio of division = 1 : 2

Step-by-step explanation:

Let's assume the point of Intersection be (x, y) and also assume that the line x+y=4 divides the line joining the given points in the ratio λ : 1.

Now, we are using section formula to find the ratio of division.

Section formula:-

  •  \sf(x,y) =  \left(  \dfrac{m_1x_2 + m_2x_1}{m_1 + m_2}, \dfrac{m_1y_2 + m_2y_1}{m_1 + m_2}  \right)

Here, m1 : m2 = λ : 1.

By substituting the values in the formula, we get:

 \sf \implies(x,y) =  \left(  \dfrac{5 \lambda + ( - 1)}{ \lambda + 1}, \dfrac{7 \lambda + 1}{ \lambda + 1}  \right)

 \sf \implies(x,y) =  \left(  \dfrac{5 \lambda  - 1}{ \lambda + 1}, \dfrac{7 \lambda + 1}{ \lambda + 1}  \right)

Now, since these coordinates are the point of Intersection, they must satisfy the given equation of line.

 \sf \implies x + y = 4

 \sf \implies  \dfrac{5 \lambda  - 1}{ \lambda + 1} +  \dfrac{7 \lambda + 1}{ \lambda + 1} = 4

 \sf \implies  \dfrac{5 \lambda  - 1 + 7 \lambda + 1}{ \lambda + 1}= 4

 \sf \implies  \dfrac{12 \lambda }{ \lambda + 1}= 4

 \sf \implies  3 \lambda =  \lambda + 1

 \sf \implies  2 \lambda =  1

 \boxed{ \sf \implies   \lambda =   \dfrac{1}{2} }

Therefore the ratio of division = λ : 1 = 1/2 : 1 or 1:2

Answered by sutarjasmin7
1

Answer:

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