the points (0,0) and (3,2) are two vertices of a polygon with integer coordinates.

Algebra
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the points (0,0) and (3,2) are two vertices of a polygon with integer coordinates. Suppose the polygon is a rectangular parallelogram. what could the other two vertices be?

Sep 3rd, 2015

Thank you for the opportunity to help you with your question!

Thank you for the opportunity to help you with your question!

The first step is to plot the points. If you do this correctly, you'll see the point (3,2) to the right, and higher, than the point (0,0). Now draw a straight line from (0,0) to (3,2). Label it A. You have one side of a parallelogram.

The key property of a parallelogram is that two opposite sides are parallel to each other. So, try drawing a straight line that is parallel to the straight line you drew earlier. One such line crosses the point (0,3), so that the second side of four COULD run from (0,0) to (0,3). Label that side B. Now you need a straight line parallel to A that runs through the point (3,2): call it C. Finally, you need a straight line parallel to B that goes through (0,3). A line, call it D, that does so starts at (3,3) and extends to the right ending at (6,2). Why? Because the distance from (0,0) to (0,3) is 3, and the length of side C must equal the length of side A.The figure looks like a rectangle that has been pushed to the right without moving the base. There are lots of other possibilities too.  In this case the other two vertices are (3,2) AND (6,2).

Please let me know if you need any clarification. I'm always happy to answer your questions.Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 3rd, 2015

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