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

Algebra ->  Parallelograms -> 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      Log On


   

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) About Me  (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.



For and :



For and :



For and :



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



through

(Left as an exercise for the student)


through



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