If the area of ` A B C` formed by `A(x , y),B(1,2)a n dC(2,1)` is 7 squae units, then prove that `x+y=15or ,x+y+9=0`

If the area of A B C formed by A(x , y),B(1,2)a n dC(2,1) is 6 squae units, then prove that x+y=15or ,x+y+9=0

If the area of DeltaABC with vertices A(x,y),B(1,2)and C(2,1) is 6 square units, then prove that x + y = 15 or x + y + 9=0.

If A(x, y), B (1, 2) and C (2, 1) are the vertices of a triangle of area 6 square units, show that x+y=15 or -9 .

If the volume of tetrahedron A B C D is 1 cubic units, where A(0,1,2),B(-1,2,1)a n dC(1,2,1), then the locus of point D is a. x+y-z=3 b. y+z=6 c. y+z=0 d. y+z=-3

If A(x_(1), y_(1)), B(x_(2), y_(2)) and C (x_(3), y_(3)) are the vertices of a Delta ABC and (x, y) be a point on the internal bisector of angle A, then prove that b|(x,y,1),(x_(1),y_(1),1),(x_(2),y_(2),1)|+c|(x,y,1),(x_(1),y_(1),1),(x_(3),y_(3),1)|=0 where, AC = b and AB = c.

If x=1+(log)_a b c ,\ y=1+(log)_b c a\ a n d\ z=1+(log)_c a b ,\ then prove that x y z=x y+y z+z xdot

If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

A triangle has its three sides equal to a , ba n dc . If the coordinates of its vertices are A(x_1, y_1),B(x_2,y_2)a n dC(x_3,y_3), show that |(x_1,y_1,2),(x_2,y_2,2),(x_3,y_3, 2)|^2=(a+b+c)(b+c-a)(c+a-b)(a+b-c)

If a ,b ,c are in G.P. and x ,y are the arithmetic means of a ,ba n db ,c respectively, then prove that a/x+c/y=2a n d1/x+1/y=2/b

Let x_(1),x_(2) are the roots of the quadratic equation x^(2) + ax + b=0 , where a,b, are complex numbers and y_(1), y_(2) are the roots of the quadratic equation y^(2) + |a|yy+ |b| = 0 . If |x_(1)| = |x_(2)|=1 , then prove that |y_(1)| = |y_(2)| =1