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 distance of the point (1,\ 2) from the mid-point of the line segment joining the points (6,\ 8) and (2,\ 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 equation of the perpendicular dropped from the point (-1, 2) onto the line joining the points (1, 4) and (2, 3).

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

A point with z-coordinate 6 lies on the line segment joining the points (2, 1, 2) and (6, 0, 8). Find the coordinates of the point.

Find the equation of a line passing through origin and parallel to the line joining the points (1,3) and (2,-1) .

A point with x-coordinate 9 lies on the line segment joining the points (8, 1, 1) and (10, -2, -3). Find the coordinates of the point.

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

The coordinates of the middle points of the sides of a triangle are (4, 2), (3, 3) and (2, 2), then coordinates of centroid are