Question

in what ratio is line segment joining (3,1) and (7,2) divided by the line x + 3y = 9

Answer 1

Let P (x, y) be the point of intersection of the line x + 3y = 9 and the line segment joined by (3,1) and (7,2)

Let (3,1) = A and (7,2) = B

Assume P divides AB in the ratio 1 : n.

By section formula we have :

P(x, y) = { (1 × x₁ + n × x₂) / (1 + n) , (1 × y₁ + n × y₂) /(1 + n) }

Doing the substitution we have :

P (x, y) = { (3 + 7n) / (1 + n) , (2 + n) / (1 + n)}

Substituting this value in the line :

x + 3y = 9

We have :

(7 + 3n) / (1 + n) + 3 { (2 + n) /(1 + n) = 9

(13 + 6n) / (1 + n) = 9

13 + 6n = 9(1 + n)

13 + 6n = 9 + 9n

9n - 6n = 13 - 9

3n = 4

n = 4/3

1 : n = 1/ (4/3)

= 3/4

The ratio is thus :

3 : 4

Answer 2

Answer:

Here is the solution in the two attachments.

Hope it helps you!