Find the coordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.

Let given coordinates be A(-4, 0) and B (0, 6).

We need to divide AB into 4 equal parts, ie first we need to find midpoint of AB, which will be D and then find out midpoints of AD and DB respectively.

Let required points be C(x₁ , y₁ ), D(x_m , y_m ) and E(x , y₂ )

By midpoint formula.

x = , y =

For midpoint D of AB,

x_m = , y_m =

∴ x_m = -2 and y_m = 3

∴ D(x_m , y_m ) ≡ (-2 , 3)

Now, for midpoint C of AD,

X₁ = , y₂ =

x₁ = -3 and y₁ = 1.5

∴C(x₁ , y₁) ≡ (-3, 1.5)

For midpoint E of DB,

X₂ = , y₂ =

∴ x₂ = -1 and y₂ = 4.5

∴ D(x₂ , y₂ ) ≡ (-1 , 4.5)

Hence the co-ordinates of the points are (-3, 1.5), (-2 , 3) and (-1 , 4.5)