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Orthocenter and circumcenter of a Delta ...

Orthocenter and circumcenter of a `Delta A B C` are `(a , b)a n d(c , d)` , respectively. If the coordinates of the vertex `A` are `(x_1,y_1),` then find the coordinates of the middle point of `B Cdot`

Text Solution

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Given are the orthocentre `H(a,b)` and the circumcentre `O(c,d)`.

`therefore` Centroid, `G=((2c+a)/(2+1),(2d+b)/(2+1))-=((2c+a)/(3),(2d+b)/(3))`

Now, centroid G divides AD in the ratio `2:`, where D is the midpoint of BC.
`therefore (2c+a)/(3)=(2x_2+x_1)/(3)`
and `(2d+b)/(3)=(2y_2+y-1)/(3)`
`therefore x_2=(2c+a -x_1)/(2),y_2=(2d+b-y_1)/(2)`
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Knowledge Check

  • The coordinate of the vertices B and C of the triangle ABC are (5,2,8) and (2, -3, 4) respectively, if the coordinates of the centroid of the triangle are (3, -1,3), then the coordinates of the vertex A are-

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