SOLUTION: Determine the point A(x,y) so that the point A(x,y), B(0,3), C(1,0), D(7,2) will be the vertices of a parallelogram. The answer is multiple choice, a. A(-6,1) b. A(3,7) c. A(

Algebra ->  Algebra  -> Graphs -> SOLUTION: Determine the point A(x,y) so that the point A(x,y), B(0,3), C(1,0), D(7,2) will be the vertices of a parallelogram. The answer is multiple choice, a. A(-6,1) b. A(3,7) c. A(      Log On

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Question 82168: Determine the point A(x,y) so that the point A(x,y), B(0,3), C(1,0), D(7,2) will be the vertices of a parallelogram. The answer is multiple choice,
a. A(-6,1)
b. A(3,7)
c. A(5,6)
d. A(6,5)
Answer by Edwin McCravy(6932) About Me  (Show Source):
You can put this solution on YOUR website!
Determine the point A(x,y) so that the point A(x,y), B(0,3), C(1,0), D(7,2)
will be the vertices of a parallelogram. The answer is multiple choice, 
a. A(-6,1)
b. A(3,7)
c. A(5,6)
d. A(6,5)

Plot the three given points:

+drawing%28440%2C400%2C-2%2C9%2C-3%2C7%2C+locate%28.5%2C-.5%2CC%281%2C0%29%29%2C+locate%286%2C1.5%2CD%287%2C2%29%29%2C%0D%0A+++%0D%0A++++locate%28-.1%2C3.2%2Co%29%2C+locate%28.9%2C0.2%2Co%29%2C+locate%286.9%2C2.2%2Co%29%2C+%0D%0A%0D%0A+++++++line%280%2C3%2C1%2C0%29%2C+line%281%2C0%2C7%2C2%29%2C++locate%28-1.5%2C3.2%2CB%280%2C3%29%29%2C+++++++%0D%0A%0D%0A++++++graph%28440%2C400%2C-2%2C9%2C-3%2C7%29+%29 

Suppose you connect them as above. Then notice
that to go from point C to point B, you have
to travel 1 unit left to (0,0) and then travel 
3 units up to B. Therefore, to go from D to A,
you must do the same. That is, you must travel
left 1 unit left to (6,2), and then travel up 
3 units to A,  So A's x-coordinate is 1 less 
than D's, and A's y-coordinate in 3 more than
D's.  So A is (6,5). That is choice (d).

+drawing%28440%2C400%2C-2%2C9%2C-3%2C7%2C+locate%28.5%2C-.5%2CC%281%2C0%29%29%2C+locate%286%2C1.5%2CD%287%2C2%29%29%2C%0D%0A+++%0D%0A++++locate%28-.1%2C3.2%2Co%29%2C+locate%28.9%2C0.2%2Co%29%2C+locate%286.9%2C2.2%2Co%29%2C+locate%286%2C5.5%2CA%286%2C5%29%29%2C+%0D%0A%0D%0A+++++++line%280%2C3%2C1%2C0%29%2C+line%281%2C0%2C7%2C2%29%2C++locate%28-1.5%2C3.2%2CB%280%2C3%29%29%2C+++++++%0D%0A%0D%0A+++++++line%287%2C2%2C6%2C5%29%2C+line%280%2C3%2C6%2C5%29%2C++%0D%0A%0D%0A++++++graph%28440%2C400%2C-2%2C9%2C-3%2C7%29+%29
 
That is the answer, but I though I might add 
that if you connect the three given points 
another way, like this:

+drawing%28440%2C400%2C-2%2C9%2C-3%2C7%2C+locate%28.5%2C-.5%2CC%281%2C0%29%29%2C+locate%286.5%2C2.9%2CD%287%2C2%29%29%2C%0D%0A+++%0D%0A++++locate%28-.1%2C3.2%2Co%29%2C+locate%28.9%2C0.2%2Co%29%2C+locate%286.9%2C2.2%2Co%29%2C+%0D%0A%0D%0A+++++++line%280%2C3%2C1%2C0%29%2C+line%280%2C3%2C7%2C2%29%2C++locate%28-1.5%2C3.2%2CB%280%2C3%29%29%2C+++++++%0D%0A%0D%0A++++++graph%28440%2C400%2C-2%2C9%2C-3%2C7%29+%29 

then there is another possible solution.  
To get it, you notice
that to go from point B to point C, you have
to travel 3 units down to (0,0) and then travel 
1 unit right to B. Therefore, to go from D to A,
you must do the same. That is, you must travel
3 units down to (7,-1), and then travel right 
3 unit to A,  So A's y-coordinate is 3 less 
than D's, and A's x-coordinate in 1 more than
D's.  So A is (8,-1). That was not one of the
choices, but it could have been.

+drawing%28440%2C400%2C-2%2C9%2C-3%2C7%2C+locate%28.5%2C-.5%2CC%281%2C0%29%29%2C+locate%286.5%2C2.9%2CD%287%2C2%29%29%2C%0D%0A+++%0D%0A++++locate%28-.1%2C3.2%2Co%29%2C+locate%28.9%2C0.2%2Co%29%2C+locate%286.9%2C2.2%2Co%29%2C+%0D%0A%0D%0A+++++++line%280%2C3%2C1%2C0%29%2C+line%280%2C3%2C7%2C2%29%2C++locate%28-1.5%2C3.2%2CB%280%2C3%29%29%2C+++++++%0D%0A%0D%0A+++++++line%281%2C0%2C8%2C-1%29%2C+line%287%2C2%2C8%2C-1%29%2C+locate%287%2C-1.5%2CA%288%2C-1%29%29%2C%0D%0A%0D%0A++++++graph%28440%2C400%2C-2%2C9%2C-3%2C7%29+%29


Believe it or not there is still another solution!!! Can you
figure out where it would be? (Hint: you'd need to extend the
graph on the left side.)

Edwin