Question

Determine the ratio in which the line 3x + y - 9 = 0 divides the line segment joining the points (1,3) and (2,7).

Answer 1

Let the line divides the points in k:1 ratio according to section formula
(2k+1/k+1, 7k+3/k+1) = (x, y)
It must satisfy the given equation so
3(2k+1/k+1) + (7k+3/k+1) = 9
6k+3+7k+3/k+1 = 9
13k+6=9k+9
13k-9k=9-6
4k=3
k=3/4

Answer 2

Answer:

Step-by-step explanation:

Suppose the line 3x + y − 9 = 0 divides the segment joining the points A(1, 3) and B(2, 7) in the ratio k : 1 at point C.

Then, the co-ordinates of C

(2k + 1/ , 7k + 3/)

k + 1 k + 1

But, C lies on 3x + y − 9 = 0.

Therefore,

2k17k3

390

k1k1

6k + 3 + 7k + 3 − 9k − 9 = 0

K = 3/4

So, the required ratio is 3 : 4

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