If the circumcentre of a triangle lies at the origin and the centroid is the middle point of the line joining the points `(a^2+1,a^2+1)` and `(2a,-2a)`,then find the orthocentre.

If the circumcenter of an acute-angled triangle lies at the origin and the centroid is the middle point of the line joining the points (a^2+1,a^2+1) and (2a ,-2a), then find the orthocentre.

If the circumcenter of an acute-angled triangle lies at the origin and the centroid is the middle point of the line joining the points (a^2+1,a^2+1) and (2a ,-2a), then find the orthocentre.

Statement-1: If the circumcentre of a triangle lies at origin and centroid is the middle point of the line joining the points (2,3) and (4,7), then its orthocentre satisfies the relation 5x-3y=0 Statement-2: The circumcentre, centroid and the orthocentre of a triangle is on the same line and centroid divides the lines segment joining circumcentre in the ratio 1:2

Find the projection of the point (1,0) on the line joining the points (-1,2) and (5,4).

Find the ratio in which point P(2,1) divides the line joining the points A (4,2) and B(8,4)

Find the distance of the point (1,\ 2) from the mid-point of the line segment joining the points (6,\ 8) and (2,\ 4) .

Find the area of a triangle ABC if the coordinates of the middle points of the sides of the triangle are (-1, -2), (6, 1) and (3, 5)

If the point P(2,1)lies on the line segment joining points A(4,2)and B(8,4), then

Find the angle between the line joining the points (1,-2), (3,2) and the line x+2y-7=0

Prove that the centroid of any triangle is the same as the centroid of the triangle formed by joining the middle points of its sides