Statement 1: If the sum of algebraic distances from point `A(1,1),B(2,3),C(0,2)` is zero on the line `a x+b y+c=0,` then `a+3b+c=0` Statement 2: The centroid of the triangle is (1, 2)

If the algebraic sum of the distances from the points (2,0), (0, 2) and (1, 1) to a variable line be zero then the line passes through the fixed point.

Statement 1: The value of alpha for which the point (alpha,alpha^2) lies inside the triangle formed by the lines x=0,x+y=2 and 3y=x is (0,1)dot Statement 2: The parabola y=x^2 meets the line x+y=2 at (0,1)dot

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:If the point (2a-5,a^2) is on the same side of the line x+y-3=0 as that of the origin, then a in (2,4) Statement 2: The points (x_1, y_1)a n d(x_2, y_2) lie on the same or opposite sides of the line a x+b y+c=0, as a x_1+b y_1+c and a x_2+b y_2+c have the same or opposite signs.

Statement 1 : The area of the triangle formed by the points A(1000 ,1002),B(1001 ,1004),C(1002 ,1003) is the same as the area formed by the point A^(prime)(0,0),B^(prime)(1,2),C^(prime)(2,1) Statement 2 : The area of the triangle is constant with respect to the translation of axes.

Find the value of a, b, c, d from the equation ((a-b,2a+c),(2a-b,3c+d))=((1,5),(0,2))

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

If the equation of the locus of a point equidistant from the points (a_1, b_1) and (a_2, b_2) is (a_1-a_2)x+(b_1-b_2)y+c=0 , then the value of c is

In A B C , the coordinates of B are (0,0),A B=2,/_A B C=pi/3, and the middle point of B C has coordinates (2,0)dot The centroid o the triangle is (a) (1/2,(sqrt(3))/2) (b) (5/3,1/(sqrt(3))) (c) (4+(sqrt(3))/3,1/3) (d) none of these

Find the orthocentre of Delta A B C with vertices A(1,0),B(-2,1), and C(5,2)