If `(x, y), (a, 0), (0, b)` are collinear, then using determinants prove that `x/a + y/b = 1` .

If points (a ,0),\ (0, b)a n d\ (x , y) are collinear, using the concept of slope prove that x/a+y/b=1.

If the points A (x,y), B (1,4) and C (-2,5) are collinear, then shown that x + 3y = 13.

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) .

If (x,y) be any point on the line segment joinijng the points (a,0)and (0,b) then prove that x/b+y/b=1.

If the points A(x , y),B(3,6)a n dC(-3,4) are collinear, show that x-3y+15=0

If the points A(x , y),B(3,6)a n dC(-3,4) are collinear, show that x-3y+15=0

If the points A(x , y),B(3,6)a n dC(-3,4) are collinear, show that x-3y+15=0

Statement -1 : If veca and vecb are non- collinear vectors, then points having position vectors x_(1) vec(a) + y_(1) vec(b) , x_(2)vec(a)+ y_(2) vec(b) and x_(3) veca + y_(3) vecb are collinear if |(x_(1),x_(2),x_(3)),(y_(1),y_(2),y_(3)),(1,1,1)|=0 Statement -2: Three points with position vectors veca, vecb , vec c are collinear iff there exist scalars x, y, z not all zero such that x vec a + y vec b + z vec c = vec 0, " where " x+y+z=0.

Consider the points O(0,0),A(0,1), and B(1,1) in the x-y plane. Suppose that points C(x,1)andD(1,y) are chosen such that 0 < x < 1. And such that O,C,andD are collinear. Let the sum of the area of triangles OAC and BCD be denoted by S. Then which of the following is/are correct?.

Show that the points (a,0),(0,b) and (x,y) are collinear if x/a+y/b=1.