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`

If the midpoints of the sides of a triangle are (2,1),(-1,-3),a n d(4,5), then find the coordinates of its vertices.

The centroid of a triangle ABC is at the point (1,1,1) . If the coordinates of A and B are (3,-5,7) and (-1,7,-6) , respectively, find the coordinates of the point C.

A,B, and C are vertice of DeltaABC,D,E and F are mid point of side AB,BC and AC respectively. If the coordinates of A, D and F are (-3,5),(5,1) and (-5,-1) respectively. Find the coordinates of B,C and E.

The equations of the perpendicular bisectors of the sides A Ba n dA C of triangle A B C are x-y+5=0 and x+2y=0 , respectively. If the point A is (1,-2) , then find the equation of the line B Cdot

The equations of the sides of a triangle are x+y-5=0, x-y+1=0, and y-1=0. Then the coordinates of the circumcenter are

If the coordinates of the vertices of triangle A B C are (-1,6),(-3,-9) and (5,-8) , respectively, then find the equation of the median through Cdot

A B C is an isosceles triangle. If the coordinates of the base are B(1,3) and C(-2,7) , the coordinates of vertex A can be (a) (1,6) (b) (-1/2,5) (c) (5/6,6) (d) none of these

Statement 1 : Let the vertices of a A B C be A(-5,-2),B(7,6), and C(5,-4) . Then the coordinates of the circumcenter are (1,2)dot Statement 2 : In a right-angled triangle, the midpoint of the hypotenuse is the circumcenter of the triangle.

A variable plane l x+m y+n z=p(w h e r el ,m ,n are direction cosines of normal ) intersects the coordinate axes at points A ,Ba n dC , respectively. Show that the foot of the normal on the plane from the origin is the orthocenter of triangle A B C and hence find the coordinate of the circumcentre of triangle A B Cdot

The coordinates of the vertices Ba n dC of a triangle A B C are (2, 0) and (8, 0), respectively. Vertex A is moving in such a way that 4tanB/2tanC/2=1. Then find the locus of A