Question

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

Answer 1

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(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 = \(\frac{-2+2}2\), y_m = \(\frac{2+8}2\)

∴ x_m = 0 and y_m = 5 

∴ D(x_m , y_m ) ≡ (0 , 5) 

Now, for midpoint C of AD,

x₁ = \(\frac{-2+0}2\), y₂ = \(\frac{2+5}2\)

x₁ = -1 and y₁ = \(\frac{7}2\)

∴C(x₁ , y₁) ≡ (-1,\(\frac{7}2\))

For midpoint E of DB,

 x₂ = \(\frac{2+0}2\), y₂ = \(\frac{8+5}2\)

∴ x₂ = 1 and y₂ = \(\frac{13}2\)

∴ E(x₂ , y₂ ) ≡ (1 ,\(\frac{13}2\))

Hence the co-ordinates of the points are (-1,\(\frac{7}2\)) , (0 , 5) and (1 ,\(\frac{13}2\) )