Statement I If sum of algebraic distances from points A(1,2),B(2,3),C(6,1) is zero on the line `ax+by+c = 0` then `2a+3b + c = 0` ,
Statement II The centroid of the triangle is (3,2)

A(-1, 3), B(4, 2) and C(3, -2) are the vertices of a triangle. Find the coordinates of the centroid G of the triangle.

The algebraic sum of distances of the line ax + by + 2 = 0 from (1,2), (2,1) and (3,5) is zero and the lines bx - ay + 4 = 0 and 3x + 4y + 5=0 cut the coordinate axes at concyclic points. Then (a) a+b=-2/7 (b) area of triangle formed by the line ax+by+2=0 with coordinate axes is 14/5 (c) line ax+by+3=0 always passes through the point (-1,1) (d) max {a,b}=5/7

The vertices of a triangle an A(1,2), B(-1,3) and C(3, 4). Let D, E, F divide BC, CA, AB respectively in the same ratio. Statement I : The centroid of triangle DEF is (1, 3). Statement II : The triangle ABC and DEF have the same centroid.

The algebraic sum of the perpendicular distances from A(x_1, y_1) , B(x_2, y_2) and C(x_3, y_3) to a variable line is zero. Then the line passes through (A) the orthocentre of triangleABC (B) centroid of triangleABC (C) incentre of triangleABC (D) circumcentre of triangleABC

Statement-1: If a, b, c in Q and 2^(1//3) is a root of ax^(2) + bx + c = 0 , then a = b = c = 0. Statement-2: A polynomial equation with rational coefficients cannot have irrational roots.

Statement-1: The orthocentre of the triangle having its verticews at A(2,0), B(4,0) and C(4,6) is at the point o(4,0) Statement-2 : Orthocentre of a right triangle is at the vertex forming a right angle

The area of a triangle is 3/2 square units. Two of its vertices are the points A (2, -3) and B(3,-2) , the centroid of the triangle lies on the line 3x - y -2 = 0 , then third vertex C is

If the algebraic sum of the distances of a variable line from the points (2,0),(0,2), and (-2,-2) is zero, then the line passes through the fixed point. (a) (-1,-1) (b) (0,0) (c) (1,1) (d) (2,2)

Statement 1: Distance of point D( 1,0,-1) from the plane of points A( 1,-2,0) , B ( 3, 1,2) and C( -1,1,-1) is 8/sqrt229 Statement 2: volume of tetrahedron formed by the points A,B, C and D is sqrt229/ 2

Statement I : The lines x(a+2b) +y(a+3b)=a+b are concurrent at the point (2,-1) Statement II : The lines x+y -1 =0 and 2x + 3y -1 = 0 intersect at the point (2,-1)