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In a Triangle ABC the coordinates of orthocentre, centroid and vertex A are respectively (2,2), (2,1) and (0,2). Then x coordinate of vertex B is

In a Triangle ABC the coordinates of orthocentre, centroid and vertex A are respectively (2,2), (2,1) and (0,2). Then x coordinate of vertex B is

Grade:11

1 Answers

Vikas TU
14149 Points
4 years ago
Dear Student,
Let, 
A (0,2) is a vertex of the ΔABC. 
O (2,2) is the orthocentre. 
D (2,1) is the centroid. 
As the vertex and orthocentre has the 
same y facilitate, we realize that the 
elevation from A to the inverse is 
parallel to the x-pivot. That is, the side 
BC is parallel to y-pivot. 
From the x directions of O and D, we realize that they are likewise parallel to y-pivot. 
Presently consider the triangles ΔAOD and ΔAFE. They are comparative. 
From the property of centroid, we have AD = 2DE. 
From the closeness of triangles, we have AO/AF = AD/AE. 
AE = AD + DE = 2DE + DE = 3DE. 
Consequently AD/AE = 2DE/3DE = 2/3. 
AO = 2. 
Consequently we have 2/AF = 2/3 => AF = 3. 
The opposite separation from vertex A to the side BC is 3 units. As A lies on the y pivot, this implies the x organize of vertex B and C of the ΔABC = 3.
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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