Question

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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 C , D and E are placed between A and B .

e.g., A____C____D_____E_____B

Here , AC = CD = DE = EB

So, C divides the line AB into 1 : 3 ratio

here A≡(-4 , 0) and B ≡(0,6)

Now, C ≡ [ (1 × 0 + 3 × -4)/(1 + 3) , (1 × 6 + 3 × 0)/(1 + 3)]

C≡(-3 , 3/2 )

Similarly , E divides the line AB into 3 : 1 ratio.

So, E ≡ [ (3 × 0 + 1 × -4)/(3 + 1) , (3 × 6 + 1 × 0)/(3 + 1)]

E ≡ (-1 , 9/2)

And D is the midpoint of AB

so, D ≡ [(-4 + 0)/2 , (0 + 6)/2 ]

D ≡ ( -2 , 3)

Answer 2

Let C , D and E are placed between A and B .

e.g., A____C____D_____E_____B

Here , AC = CD = DE = EB

So, C divides the line AB into 1 : 3 ratio

here A≡(-4 , 0) and B ≡(0,6)

Now, C ≡ [ (1 × 0 + 3 × -4)/(1 + 3) , (1 × 6 + 3 × 0)/(1 + 3)]

C≡(-3 , 3/2 )

Similarly , E divides the line AB into 3 : 1 ratio.

So, E ≡ [ (3 × 0 + 1 × -4)/(3 + 1) , (3 × 6 + 1 × 0)/(3 + 1)]

E ≡ (-1 , 9/2)

And D is the midpoint of AB

so, D ≡ [(-4 + 0)/2 , (0 + 6)/2 ]

D ≡ ( -2 , 3)