How to Organize Coordinate Proofs in Geometry

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Organizing coordinate proofs in geometry is something that you would want to do by paying close attention to their numerical values. Organize coordinate proofs in geometry with help from an experienced math professional in this free video clip.

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Hi. I'm Drew Moyer and this is how to organize coordinate proofs in geometry. Coordinate proofs have been given variables for coordinates instead of numerical values. But we're still required to prove something about the graph. So here we have quadrilateral LMNO. And we're required to prove that this quadrilateral is a parallelogram. Well, I can prove something's a parallelogram if I can prove that both sets of opposite sides are parallel to each other. Let's start with the tops and bottoms. LM and ON. And if I can prove that their slopes are the same then they must be parallel. So let's start with LM and I want to take the second y coordinate which is M minus the first y coordinate which is M over the second x coordinate which is z plus l over the second x coordinate which is z plus l and the first x coordinate which is l. And simplify that and I would get that LM is equal to m minus m which is zero over z plus l minus l which is just z which equals zero. So the slope of LM is zero, aka a horizontal line. Let's see what the slope of ON is. Again we want to take the second y coordinate, zero and the first y coordinate, zero, subtract then and then I want to have the second x coordinate z, minus zero which is the first x coordinate. And I would get that ON is equal to zero minus zero which is zero over z which again is zero. So LM and ON have the same slope. Therefore they must be parallel. So I'll go ahead and mark that on my graph. Now we want to see if OL is parallel to NM. So let's take a look. Again I want to take the second y coordinate which is M, subtract the first y coordinate which is zero and then I want to take the second x coordinate, L minus the first x coordinate, zero and I get that the slope of OL is equal to M over L. So let's keep that in mind and move on to our next line which is MN. And again, we want to take the second y coordinate M minus the first y coordinate, zero over the second x coordinate which is z plus L minus the first x coordinate which is z. And then we're just going to simplify, M minus zero is M and z plus L minus z is L. So we have all 4 slopes now and as you can see OL and MN have the same slope which means that they must be parallel. So now I have proven both sets of opposite sides parallel to each other and therefore quadrilateral LMNO is a parallelogram. So, I'm Drew Moyer and this is how to organize coordinate proofs in geometry.

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