Question

The point of trisection of the line segment joining (6,-3),(-3,9) is.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Concept:

In coordinate geometry, the section formula is used to find the ratio in which a line segment is split by an internal or external point. It is used to find out the centroid, incenter and excenters of a triangle. In physics, it is used to locate the mass center of systems, balance points, etc.

Trisection means dividing the line into three equal parts.

Let the point dividing be(x,y)

x=(m₁x₂+m₂x₁)/(m₁+m₂)

y=(m₁y₂+m₂y₁)/(m₁+m₂)

Given:

line segment joining (6,-3),(-3,9)

Find

P,Q(the points of trisection)

Solution:

AP=PQ=QB

So. let p be (x₁,y₁) and Q be (x₂,y₂)

a₁=6,b₁=-3

a₂=-3,b₂=9

For P, AP:PB=1:2

x₁=(1x(-3)+2x6)/3

  =3

y₁=(1x9+2x(-3))/3

  = 1

For Q,AQ:QB=2:1

x₂=(2x(-3)+1x6)/3

  =0

y₂=(2x9+1x(-3))/3

   =5

Therefore,P=(3,1) and Q=(0,5)

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