The points A ( - 6, 10), B ( - 4, 6) and C (3, - 8) are collinear such that


True

We know by the rule that, area of a triangle formed by the points (x1, y1), (x2, y2) and (x3, y3) is zero, then the points are collinear.


Area of the triangle = 1/2 [x1 (y2 - y3 ) + x2 (y3 - y1 ) + x3 (y1 - y2 )]


Here we have;


x1 = - 6


x2 = - 4


x3 = 3


and


y1 = 10


y2 = 6


y3 = - 8


Area of the triangle ∆ ABC = 1/2 [ - 6 {6 – ( - 8)} + ( - 4) ( - 8 – 10) + 3(10 – 6)]


= 1/2 [ - 6(14) + ( - 4) ( - 18) + 3(4)]


= 1/2 ( - 84 + 72 + 12) = 0


So, given points are collinear.


Now,


Calculate the distance between A ( - 6, 10) and B ( - 4, 6);


Distance between the points (x1, y1) and (x2, y2);







Distance between A ( - 6, 10) and C (3, - 8);







AB=2/9 AC


10
1