Question 1207839: 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)?
Found 4 solutions by math_tutor2020, mccravyedwin, ikleyn, Edwin McCravy:
Answer by math_tutor2020(3817)   (Show Source):
Answer by mccravyedwin(408)  (Show Source):
You can put this solution on YOUR website!
It's always a good idea to draw a graph if the question is about points
and lines. The red line is AB, the green line is BC, The black line is
AC. I drew a little off from the others, but it's really the sum of the
other two lines. The other tutor has told you enough about how you are
to prove what you want with the distance formula.
Edwin
Answer by ikleyn(52812)  (Show Source):
You can put this solution on YOUR website! .
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)?
~~~~~~~~~~~~~~~~~~~~~
The problem can be easily solved without the distance formula,
which is, actually, non-necessary and excessive calculation job.
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.
Solved, by a simple way.
Answer by Edwin McCravy(20060)  (Show Source):
|
|
|
