If `|x_1y_1 1x_2y_2 1x_3y_3 1|=|a_1b_1 1a_2b_2 1a_3b_3 1|` then the two triangles with vertices `(x_1, y_1),(x_2,y_2),(x_3,y_3)` and `(a_1,b_1),(a_2,b_2),(a_3,b_3)` are equal to area (b) similar congruent (d) none of these

|(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)|=|(a_1,b_1,1),(a_2,b_2,1),(a_3,b_3,1)| then the two triangles with vertices (x_(1), y_(1)), (x_(2), y_(2)), (x_(3), y_(3)) and (a_(1), b_(1)), (a_(2), b_(2)), (a_(3), b_(3)) are

The centroid of the triangle with vertices at A(x_(1),y_(1)),B(x_(2),y_(2)),c(x_(3),y_(3)) is

If |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=|{:(a_(1),b_(1),1),(a_(2),b_(2),1),(a_(3),b_(3),1):}| , then the two triangles with vertices (x_(1),y_(1)) , (x_(2),y_(2)) , (x_(3),y_(3)) and (a_(1),b_(1)) , (a_(2),b_(2)) , (a_(3),b_(3)) must be congruent.

if |[2a,x_1,y_1],[2b,x_2,y_2],[2c,x_3,y_3]|=(abc)/2!=0 then the area of the triangle whose vertices are (x_1/a,y_1/a),(x_2/b,y_2/b),(x_3/c,y_3/c) is (A) (1/4)abc (B) (1/8)abc (C) 1/4 (D) 1/8

If (b_2-b_1)(b_3-b-1)+(a_2-a_1)(a_3-a_1)=0 , then prove that the circumcenter of the triangle having vertices (a_1,b_1),(a_2,b_2) and (a_3,b_3) is ((a_2+a_3)/(2),(b_2+b_3)/(2)) .

If a_1x+b_1y+c_1z=0, a_2x+b_2y+c_2z=0, a_3x+b_3y+c_3z=0 and |(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|=0 , then the given system then