Question

10. Find the points which divide the line segment joining A(-4 ,0) and B (0,6) into 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

Solution :

Given A( -4 ,0 ) , B( 0 , 6 )

i ) Q is the midpoint of A and B ,then

Coordinates of Q

= [ (-4+0)/2 , (0+6)/2 ]

= ( -2 , 3 )---( 1 )

ii ) P is the midpoint of AQ, then

Coordinates of P

= [ ( -4 -2 )/2 , ( 0+3)/2 ]

= ( -3 , 3/2 )

iii ) R is the midpoint of QB , then

Coordinates of R

= [ (-2+0)/2 , ( 3 + 6 )/2 ]

= ( -1 , 9/2 )

Therefore ,

Required three points are ,

P( -3 , 3/2 ) , Q( -2 , 3 ) and

R( -1 , 9/2 )

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