Answer :

Let the line segment joining the points A (–4, 0) and B (0, 6) be divided into 4 parts by points P (x_{1}, y_{1}), Q (x_{2}, y_{2}) and R(x_{3}, y_{3}).

Clearly, P divides the line segment AB internally in the ratio1:3.

∴ By internal division formula,

x_{1} = = –3

y_{1} =

Again, Q divides the line segment AB internally in the ratio 1:1.

∴ By mid–point formula,

x_{2} = = –2

y_{2} = =3

Also, R divides the line segment AB internally in the ratio3:1.

∴ By internal division formula,

x_{3} = = –1

y_{3} =

∴ The required points are P , Q (–2, 3)and R .

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