Math  explanation
posted by Anonymous .
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
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
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
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(35),y(4+1)=
AB(8,5)
C(13x,6y)B(3x,4y)=x(13+3),y(64)=
BC(16,10)
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