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

If the points A (x,y),(-1,3)and(5,-3) ar collinear, then show that x + y = 2.

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_2x_3)+(y_3-y_1)/(x_3x_1)+(y_1-y_2)/(x_1x_2)=0

Show that the points A(1,3,2),B(-2,0,1) and C(4,6,3) are collinear.

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.

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

Show that the points A (2, 3, 4), B (3, 4, 6) and C (5, 6, 16) are collinear.

The distance of point P(x, y) from the points A(1, -3) and B(-2, 2) are in the ratio 2 : 3. Show that 5x^(2) + 5y^(2) - 34x + 70y + 58 = 0 .

STATEMENT-1: If three points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) are collinear, then |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=0 STATEMENT-2: If |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=0 then the points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) will be collinear. STATEMENT-3: If lines a_(1)x+b_(1)y+c_(1)=0,a_(2)=0and a_(3)x+b_(3)y+c_(3)=0 are concurrent then |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|=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