Determine the ratio in which the line 3x + y – 9 = 0 divide the segm

1.	Determine the ratio in which the line 3x + y – 9 = 0 divide the segment joining the points (1, 3) and (2, 7).
Answer» Let the of division k : 1 as and point then the coordinates of the points are ((2k + 1)/(k + 1), (7k + 3)/(k + 1)) But the point ‘C’ lies on 3x + y – 9 = 0 ⇒ 3((2k + 1)/(k + 1)) + (7k + 3)/(k + 1) - 9 = 0 = 6k + 3 + 7k + 3 - ⇒ 9k - 9 = 0 ⇒ 4x - 3 = 0 k = 3/4 ∴ The required ratio is 3 : 4 internally

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

Answer»

Let the of division k : 1 as and point then the coordinates of the points are ((2k + 1)/(k + 1), (7k + 3)/(k + 1))

But the point ‘C’ lies on 3x + y – 9 = 0

⇒ 3((2k + 1)/(k + 1)) + (7k + 3)/(k + 1) - 9 = 0 = 6k + 3 + 7k + 3 - ⇒ 9k - 9 = 0

⇒ 4x - 3 = 0

k = 3/4

∴ The required ratio is 3 : 4 internally