Question

find the ratio in which the line segment joining the points (-3,10) &(6,-8) is divided by (-1,6)

Answer 1

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Answer 2

Answer:-

Given:

( - 1 , 6) divided the line segment joining the points (- 3 , 10) & (6 , - 8).

Using section formula;

i.e., The co - ordinates of a point which divides the line segment joining the points (x₁ , y₁) & (x₂ , y₂) in the ratio m : n are :

(x , y) = [ mx₂ + nx₁ / m + n , my₂ + ny₁ / m + n ]

Let,

• x₂ = 6

• x₁ = - 3

• y₂ = - 8

• y₁ = 10

• m = m

• n = n.

• x = - 1

• y = 6.

Hence,

⟶ (- 1 , 6) = [ {m(6) + n( - 3)} / m + n , {m(- 8) + n(10)} / m + n ]

⟶ (- 1 , 6) = [ (6m - 3n) / m + n , ( - 8m + 10n) / m + n ]

★ - 1 = 6m - 3n/m + n

⟶ - 1(m + n) = 6m - 3n

⟶ - m - n = 6m - 3n

⟶ - m - 6m = - 3n + n

⟶ - 7m = - 2n

⟶ (- 7/ - 2) * (m/n) = 1

⟶ m/n = 2/7

⟶ m : n = 2 : 7

Therefore, the ratio in which the line segment is divided is 2 : 7.