Question 1207839
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The coordinates of points A, B, and C are A(-4, 6), B(-1, 2), and C(2,-2). 

(a) Show that AB = BC by using the distance formula. 

(b) Show that AB + BC = AC by using the distance formula. 

(c) What can you conclude from parts (a) and (b)?
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        The problem can be easily solved without the distance formula, 

        which is, actually, non-necessary and excessive calculation job.



<pre>
Vector AB with starting point A and ending point B is

    <(-1-(-4),2-6> = <3,-4>.


Vector BC with starting point B and ending point C is

    <(2-(-1),-2-2> = <3,-4>.


Thus vectors AB and BC are congruent: they represent the same vector.


It implies that


(a)  Their lengths are the same, AB = BC  (without using the distance formula).


(b)  AB + BC = AC                         (without using the distance formula).


(c)  The conclusion is that three points A, B and C lie on the same straight line and point C is the midpoint of segment AC.
</pre>

Solved, &nbsp;by a simple way.