Question

Find the co-ordinates of the points of trisection of the line segment AB with A(2,7) and B(-4,-8).

Answer 1

Let C and D are placed in line joining points A and B in such a way that
AC = CD = DB .
e.g., A --------------C----------------D-------------B
Here C divides line AB in 1 : 2 ratio
so use section formula,
C = [ (1 × -4 + 2 × 2 )/(1 + 2) , (1 × -8 + 2 × 7)/(1 + 2) ]
= [ (-4 + 4)/3 , (-8 + 14)/3 ]
= (0, 2)

Also D divides the line AB in 2 : 1 ratio .
So, D = [ (2 × -4 + 1 × 2)/(2 + 1), ( 2 × -8 + 1 × 7)/(2 + 1) ]
= [(-8 + 2)/3 , (-16 + 7)/3]
= (-2, -3)

Answer 2

Step-by-step explanation:

Let C and D are placed in line joining points A and B in such a way that

AC = CD = DB .

e.g., A --------------C----------------D-------------B

Here C divides line AB in 1 : 2 ratio

so use section formula,

C = [ (1 × -4 + 2 × 2 )/(1 + 2) , (1 × -8 + 2 × 7)/(1 + 2) ]

= [ (-4 + 4)/3 , (-8 + 14)/3 ]

= (0, 2)

Also D divides the line AB in 2 : 1 ratio .

So, D = [ (2 × -4 + 1 × 2)/(2 + 1), ( 2 × -8 + 1 × 7)/(2 + 1) ]

= [(-8 + 2)/3 , (-16 + 7)/3]

= (-2, -3)