Find the coordinates of the points which divide the line segment joining A (-2, 2) and B (2, 8) into four equal parts.

Let given coordinates be A(-2, 2) and B (2, 8).

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 = 0 and y_m = 5

∴ D(x_m , y_m ) ≡ (0 , 5)

Now, for midpoint C of AD,

X₁ = , y₂ =

x₁ = -1 and y₁ =

∴C(x₁ , y₁) ≡ (-1, )

For midpoint E of DB,

X₂ = , y₂ =

∴ x₂ = 1 and y₂ =

∴ E(x₂ , y₂ ) ≡ (1 , )

Hence the co-ordinates of the points are (-1, ) , (0 , 5) and (1 , )