Question

determine the ratio in which the line 3x+y-9=0 divides the 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

Ratio= 3:4

Answer 2

Answer:

Step-by-step explanation:

Let the ratio be k:1

Coordinates of the point dividing the line segment =

        x coordinate=  (mx2+nx1/m+n) {this is the formula. Here m and n are the ratio. x2 and x1 are coordinates)

      y coordinate= (my2+my1/m+n)

So x = (k*2+ 1*1/k+1) = (2k+1/k+1) { Substitute values in above equation}

    y = (k*7+1*3/k+1) = (7k+3/k+1)

Substitute values of x and y in the equation given in the question,

3x+y-9=0

3(2k+1/k+1)+(7k+3/k+1)-9 = 0

(6k+3/k+1) + (7k+3/k+1) = 9

(6k+3+7k+3/k+1) = 9

13k+6/k+1 = 9

13k+6 = 9(k+1)

13k+6=9k+9

13k-9k = 9-6

4k = 3

k= 3/4

So the ratio k:1 = 3:4

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