# 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

Vikas TU
14149 Points
7 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)