Find the coordinates of points dividing the line segment joining the points (–4, 0) and (0, 6) into 4 equal parts.

Let the line segment joining the points A (–4, 0) and B (0, 6) be divided into 4 parts by points P (x₁, y₁), Q (x₂, y₂) and R(x₃, y₃).

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

∴ By internal division formula,

x₁ = = –3

y₁ =

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

∴ By mid–point formula,

x₂ = = –2

y₂ = =3

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

∴ By internal division formula,

x₃ = = –1

y₃ =

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