Question

find the ratio in which the line 3 X + y - 9 = 0 divides the line segment joining points 1,3 and 2,7
Expain in detail​

Answer 1

Let the line divides the points in k:1 ratio according to section formula

Let the line divides the points in k:1 ratio according to section formula(2k+1/k+1, 7k+3/k+1) = (x, y)

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

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 so3(2k+1/k+1) + (7k+3/k+1) = 9

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 so3(2k+1/k+1) + (7k+3/k+1) = 96k+3+7k+3/k+1 = 9

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 so3(2k+1/k+1) + (7k+3/k+1) = 96k+3+7k+3/k+1 = 913k+6=9k+9

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 so3(2k+1/k+1) + (7k+3/k+1) = 96k+3+7k+3/k+1 = 913k+6=9k+913k-9k=9-6

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 so3(2k+1/k+1) + (7k+3/k+1) = 96k+3+7k+3/k+1 = 913k+6=9k+913k-9k=9-64k=3

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 so3(2k+1/k+1) + (7k+3/k+1) = 96k+3+7k+3/k+1 = 913k+6=9k+913k-9k=9-64k=3k=3/4