Area of triangle formed by `(x_1,y_1), (x_2, y_2),((x_1 +kx_2)/(1+k), (y_1+ ky_2)/( 1+k))` is

Area of the triangle formed by (x_(1),y_(1)),(x_(2),y_(2)),(3x_(2)-2x_(1),3y_(2)-2y_(1)) (in sq.units) is

Prove that the area of the triangle formed by the tangents at (x_(1),y_(1)),(x_(2)) "and" (x_(3),y_(3)) to the parabola y^(2)=4ax(agt0) is (1)/(16a)|(y_(1)-y_(2))(y_(2)-y_(3))(y_(3)-y_(1))| sq.units.

Write the formula for the area of the triangle having its vertices at (x_1,\ y_1),\ \ (x_2,\ y_2) and (x_3,\ y_3) .

The orthocentre of triangle formed by lines x+y-1=0, 2x+y-1=0 and y=0 is (h, k), then (1)/(k^(2))=

The orthocentre of triangle formed by lines x+y-1=0, 2x+y-1=0 and y=0 is (h, k), then (1)/(k^(2))=

The coordinates of any point on the line-segment joining the points ( x _(1) ,y_(1) , z_(1)) and (x_(2), y_(2),z_(2)) are ((x_(1)+kx_(2))/(k + 1),(y _(1) + ky_(2))/(k + 1),(z_(1)+kz_(2))/(k + 1)) , then the value of k will be _

The area of the triangle formed by the lines x^(2 )+4 x y+y^(2)=0, x+y=1 is