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 circumcentre of a triangle lies at the point (a, a) and the centroid is the mid - point of the line joining the points (2a+3, a+4) and (a-4, 2a-3) , then the orthocentre of the triangle lies on the line

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

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 acute angle between x-axis and the straight line joining the points (1, 1, 3) and (3, 2, 1).

if a vertex of a triangle be(1,1) and the middle point of the sides through this point are(-2,3) and (5,2) , find the other vertices

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

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.

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.

If a vertex of a triangle is (1,1) , and the middle points of two sides passing through it are -2,3) and (5,2), then find the centroid of the triangle.