Question 723802: Points A, B and C have the coordinates (1,6), (0,0) and (-2,2). Find 3 possible coordinates for a point D so that the four points form a parallelogram . Exclude the case where all points lie in a straight line. How do you work this out? Thanks, Lizzy.
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! The question is open ended, since there can be four other points to choose. Either imagine or plot on paper, the three given points, and choose where you wish to pick the fourth vertex of the parallelogram. This point will be an end point of a segment parallel to another defined line among your given set of points.
You may easily imagine the desired point directed from (1,6), and on a segment parallel to the line defined by (0,0) & (-2,2). Find the equation of the line with this slope and which contains (1,6).
You now want to get an equation of another line; the line has the same slope as the two points (0,0) & (1,6) but contains the point (-2,2).
ANSWER THIS QUESTION: At what point do these two lines intersect? THAT will be the point of the fourth vertex for one of the possible parallelograms.
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