Q. 114.5( 14 Votes )

# Find in what ratio does the line 3x + y = 9 divide the line segment joining the points (1, 3) and (2, 7)?

Answer :

Let the line segment joining (1, 3) and (2, 7) be divided by the given line in the ratio λ : 1 at point P (x, y).

By internal division formula

x =

y =

Since P lies on the line 3x + y = 9, it must satisfy its equation.

Hence, 3× = 9

6λ +3 + 7λ +3 = 9 (λ + 1)

13λ + 6 = 9λ + 9

4λ = 3

⇒ λ =

∴ Required ratio is =3:4.

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