Question

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

Answer 1

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(x₂ , y₂ )

By midpoint formula.

x = \(\frac{x_1+x_2}2\), y = \(\frac{y_1+y_2}2\)

For midpoint D of AB,

 x_m = \(\frac{-4+0}2\), y_m = \(\frac{0+6}2\)

∴ x_m = -2 and y_m = 3 

∴ D(x_m , y_m ) ≡ (-2 , 3) 

Now, for midpoint C of AD,

x₁ = \(\frac{-4-2}2\), y₂ = \(\frac{0+3}2\)

x₁ = -3 and y₁ = 1.5 

∴C(x₁ , y₁) ≡ (-3, 1.5) 

For midpoint E of DB,

x₂ = \(\frac{0-2}2\), y₂ = \(\frac{6+3}2\)

∴ 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)