SOLUTION: For A(-2,-4), B(-5,-1), and C(0,-4). find all locations of a fourth point, D, so that a paralleogram is formed using A, B, C, D in any order as vertices. Plot each point D on a coo
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Question 186973: For A(-2,-4), B(-5,-1), and C(0,-4). find all locations of a fourth point, D, so that a paralleogram is formed using A, B, C, D in any order as vertices. Plot each point D on a coodinate grid and draw the parallelogram.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Since you are given 3 points, you can select 3 pairs of points. Using the two-point form of the equation of a line, you can create three equations representing three lines.
(x - x_1) )
For )
and )
:
(x + 2) \ \ \Rightarrow\ \ y = -x -6)
For and )
:
(x + 5) \ \ \Rightarrow\ \ y = -\frac{3}{5}x -4)
For and :
(x + 2) \ \ \Rightarrow\ \ y = - 4)
Now, using:
Create the equation of the parallel to each of the above lines through the given point not on that line using the point-slope form of the equation of a line:
through :)
 \ \ \Rightarrow\ \ y = -x -4)
through :)
(Left as an exercise for the student)
through
 \ \ \Rightarrow\ \ y = -1)
Now that we have 
and 
we only need to find the point of intersection between 
and 
Since we know that
from the equation for , we can just substitute into the equation for :
Hence, Point D for the first parallelogram is (-3,-1).
Now all you have to do is derive the equation for 
and find the points of intersection with the other two lines to get the other two coordinate pairs for the other two possibilities for Point D.
John
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