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

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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