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 (x_{1}, y_{1}), (x_{2}, y_{2}) and (x_{3}, y_{3}) is zero, then the points are collinear.

Area of the triangle = 1/2 [x_{1} (y_{2} - y_{3} ) + x_{2} (y_{3} - y_{1} ) + x_{3} (y_{1} - y_{2} )]

Here we have;

x_{1} = - 6

x_{2} = - 4

x_{3} = 3

and

y_{1} = 10

y_{2} = 6

y_{3} = - 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 (x_{1}, y_{1}) and (x_{2}, y_{2});

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

∴ AB=2/9 AC

10