Question

Find the ratio in which the line x
+ 3y - 14 = 0 divides the line
segment joining the points
A(-2,4) and B(3,7)​

Answer 1

we have to find the ratio in which the line x + 3y - 14 = 0 divides the line segment joining the points A(-2, 4) and B(3, 7).

solution : let point of division divides the line into k : 1 ratio.

using formula, (x , y) = [(kx₂ + x₁)/(k + 1), (ky₂ + y₁)/(k + 1)]

here (x₁ , y₁) = (-2, 4) and (x₂ , y₂) = (3, 7)

so, (x , y) = [(3k - 2)/(k + 1), (7k + 4)/(k + 1)]

now putting (x , y) in the equation x + 3y - 14 = 0.

so, (3k - 2)/(k + 1) + 3(7k + 4)/(k + 1) - 14 = 0

⇒(3k - 2) + (21k + 12) - 14(k + 1) = 0

⇒10k - 4 = 0

⇒k = 2/5

Therefore the ratio in which the given line divides the line segment is 2 : 5.

also read similar questions : Find the ratio in which the line x+3y-14=0 divides the line segment joining the points A(-2,4) B(3,7).

https://brainly.in/question/1594798

Determining the ratio in which the line 2x+y-4=0 divides the line segment joining the points A(2,-2) and B(3,7).

https://brainly.in/question/23930521