If `(a, b), (x, y), (p,q)` are the coordinates of circumcentre, centroid, orthocentre of the triangle then

If (alpha, beta) , (bar x, bar y) and (p, q) are the coordinates of the circumcentre, the centroid and the orthocentre of a triangle, prove that : 3barx=2alpha + p and 3bary= 2beta+q .

Let A(a,b),B(3,4) and C(-6,-8) respectively denote the centroid,circumcentre and orthocentre of a triangle.Then,the distance of the point P(2a+3,7b+5) from the line 2x+3y-4=0 measured parallel to the line x-2y-1=0 is

If coordinates of the circum centre and the orthocentre of a triangle respectively (5,5) and (2,2) then the coordinates of the centroid are

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

If coordinates of the circumcentre and the orthocentre of a triangle are respectively (5, 5) and (2, 2), then the coordinates of the centroid are

Assertion (A) If (-1, 3, 2) and (5, 3, 2) are respectively the orthocentre and circumcentre of a triangle, then (3, 3, 2) is its centroid. Reason ( R ) Centroid of the triangle divides the line segment joining the orthocentre and the circumcentre in the ratio 1 : 2. Which one of the following is true ?