Posted by **Anonymous** on Saturday, March 29, 2008 at 4:42pm.

This is an example in the text book.

Using vectors, demonstrate that the three points A(5, -1), B(-3,4) and C(13,-6) are collinear.

Solution

AB = (-8, 5)

BC = (16, -10)

Then BC = 2AB

AB and BC have the opposite direction, so the points A, B, and C must be collinear.

I don't understand how AB = (-8, 5) and

BC = (16, -10)

- Math - explanation -
**Damon**, Saturday, March 29, 2008 at 5:35pm
vector AB is (-3 -5) i + (4 - (-1) ) j

= -8 i + 5 j

vector BC is (13 - (-3)) i + (-6 - 4) j

= 16 i - 10 j

- Math - explanation -
**Damon**, Saturday, March 29, 2008 at 5:37pm
Now the lines are collinear because they go through the same point (point B)

and they have the same slope (although one is going down the hill while the other goes up)

- Math - explanation -
**Amanda**, Saturday, March 29, 2008 at 5:38pm
I'm not sur if this will help, but to get AB, you subtract A from B and B from C.

B(-3x,4y)-A(5x,-1y)=x(-3-5),y(4+1)=

AB(-8,5)

C(13x,-6y)-B(-3x,4y)=x(13+3),y(-6-4)=

BC(16,-10)

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