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Let A(4,2). B(6,5) and C(1,4) be the vertices of AABC
The median from Ameets BC at D. Find the coordinates of the
point D.
Find the coordinates of the point Pon AD such that AP: PD=
2:1.
nent BE in the ratio 2:1 and also that
3. Find the points which divide the line segment BE in the
line segment CF in the ratio 2:1.
4. What do you observe ?
Justify the point that divides each median in the ratio 2:1 is the centriod of
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The coordinate of point D is (7/2,11/2)
The coordinates of the point P on AD such that AP:PD =2:1 is (11/3,11/3) .
The point which divide the line segment BE and line segment CF in the ratio 2:1 is (11/3,11/3)
We observe that the median intersect at a common point called the centroid
- The point of intersection of all the median of a triangle is called the centroid .
- Centroid divides the line segment in the ratio of 2:1.
- So the given point P is the centroid of the triangle having coordinates [(x₁+x₂+x₃)/3 , (y₁+y₂+y₃)/3]
- P = [ (4+6+1)/3 , (2+5+4)/3 ]
= [ 11/3 , 11/3 ]
- Now by using the section formula we will find the coordinates of point D
- x = (mx₂+nx₁)/(m+n) y = (my₂+ny₁)/(m+n)
- where x and y are coordinates of the point dividing the line segment.
- For D m:n = 2:1 m=2 and n=1
x₁,y₁ = (4,2) and (x,y)=(11/3 , 11/3)
- Now by putting the given values in the above equation we will get the coordinates of D as (7/2 ,9/2)
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