`A (3,4 ), B (-3, 0) and C (7, -4)` are the vertices of a triangle. Show that the line joining the mid-points `D (x_1, y_1), E (x_2, y_2) and F (x, y)` are collinear. Prove that `(x-x_1) (y_2 - y_1) = (x_2 - x_1) (y-y_1)`

Three points A(x_1 , y_1), B (x_2, y_2) and C(x, y) are collinear. Prove that: (x-x_1) (y_2 - y_1) = (x_2 - x_1) (y-y_1) .

Three points (x_(1),y_(1)),B(x_(2),y_(2)) and C(x,y) are collinear.Prove that (x-x_(1))(y_(2)-y_(1))=(x_(2)-x_(1))(y-y_(1))

If the points (x_1, y_1), (x_2, y_2) and (x_3, y_3) be collinear, show that: (y_2 - y_3)/(x_2 x_3) + (y_3 - y_1)/(x_3 x_2) + (y_1 - y_2)/(x_1 x_2) = 0

If A(x_(1),y_(1)),B(x_(2),y_(2)) and C(x_(3),y_(3)) are the vertices of a triangle then excentre with respect to B is

Show that the equation of the chord of the parabola y^2 = 4ax through the points (x_1, y_1) and (x_2, y_2) on it is : (y-y_1) (y-y_2) = y^2 - 4ax

If A(x_(1),y_(1)),B(x_(2),y_(2)),C(x_(3),y_(3)) are the vertices of the triangle then show that:'

If (x,y) be on the line joining the two points (1,-3) and (-4,2), prove that x+y+2=0

If the points (x_(1),y_(1)),(x_(2),y_(2)), and (x_(3),y_(3)) are collinear show that (y_(2)-y_(3))/(x_(2)x_(3))+(y_(3)-y_(1))/(x_(3)x_(1))+(y_(1)-y_(2))/(x_(1)x_(2))=0

If A(x_1, y_1), B (x_2, y_2) and C (x_3, y_3) are the vertices of a DeltaABC 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 .