 I'm asked in this video to find the missing coordinates in three parallelograms. We've done this before, but I just want to remind you, and we're talking about the X values that's going to represent the horizontal distance. And if you want to even draw the little horizontal line to remind yourself, and when we're talking about the Y values, that's going to be the vertical distance. And if you want to draw the little vertical line to remind yourself, that could be helpful. Note, too, that in the directions it says, use the same variable when it's appropriate and introduce a new variable when needed. This introduce a new variable means, in previous problems, we've added a letter or added a variable when we didn't have enough information, and that's what that's talking about. I'll tell you right now, though, that for these three problems, we will not have to introduce a new variable. So in this rectangle, we're only given information about one of the vertices here, and that's going to be enough to fill in the missing three pieces here. I'm going to start with the X value here. This says negative C, and that represents the distance right here. Note that it's negative. All that that means is we know that that point is in the second or third quadrant. We're going left from the origin. So that point is going to be a negative X value, but this distance is going to be C because distance is always a positive value. If that distance is C, that means this distance below is also C, and because these congruency marks are here, I can fill in this measure as C, and then of course up here this measure is also C. Then I can go to my Y value here of E that represents my vertical distance, and so because this is a rectangle, any of these vertical distances on the rectangle will each have a measure of E. And now I can go ahead and fill in my missing values. I'll start with point R. It doesn't matter where I start. If I am starting at the origin to get to point R, I'm going to go horizontally a measure of C, and then I'm not going up or down, so my vertical distance will be zero. So I can go ahead and fill that in, C zero. And next I'll go to point P because that's going to be similar. If I'm starting at the origin and going out to point P, I'm also going a distance of C, but because I'm going left on the origin, anytime I'm going left from the origin horizontally that will be a negative value, and point P I'm not going up or down so that will be zero as well. And so to finish up with point A here, if I start at the origin, I can see visually from all my measures I'm going to go out C and up E. And so it does help to go ahead and fill in those values, even though you might not need to on some of the problems. I can do a quick check at the end because remember for parallelograms, these Y values will be the same both on top and on bottom, zero zero and EE. Going on, I'm given a parallelogram with two points where the values are given to me. I'm going to start here because I know that A means that this horizontal distance is A and because parallelograms have congruent sides, I can fill in that side as well. Next I'll go up to point E and I'm actually going to start with the Y value. The Y value represents my vertical distance and so any vertical piece on my parallelogram will have a measure of C. I'm also going to put it over here. This will help me later when I find that missing value. So every vertical measure there is C and then the last piece that is given to me is that value of B. That represents the horizontal distance. If I put it in this imaginary line where I had my C, this is the horizontal distance that I need to use if I want to get up to point E here. So I can fill in that this value is B and then this will be helpful because of the symmetry. This value over here is B as well and now we can go ahead and fill in the missing values. I'm going to start with the origin because that one's the easy one, zero zero. Point L is at the origin and then I'll move up to that point O. I know to get to point O if I'm starting at the origin, I'm going to go out this distance and then go up. This distance here is represented by A plus B and then I'm going to go up C. That's why it's helpful to write those values down. So I know my X value is A plus B, Y value of C. I can check my Y values up here are the same C and C Y values down below zero and zero and remember before we said that this X value plus this X value would equal this X value. That's another nice quick check. B plus A is the same as A plus B. Moving on to the last one, this is another parallelogram. A little more complicated, I have three values here and that's all I will need for this problem. I won't have to introduce new values at all. I'm going to start with this value of M. I know represents this horizontal distance here and then because the opposite sides are congruent I can fill in that as well. Next I'll go up here to this negative N. Remember it's only negative because it's left of the origin. This represents a distance of N going left from that Y axis. And because this is N, remember I can fill in this imaginary line here and make this value N as well. My last piece then will be this value of R represents the vertical measure of my parallelogram. It will be R and that will represent any vertical measure in my parallelogram that I'll need. So now I can go ahead and fill in my missing values. The origin of course, zero zero. And then if I fill in the value of G, this is where all my values I write on here will be helpful because I'm trying to get to this point. This point represents this horizontal distance here which we don't have. But we do know that this measure is M and if we come back from that measure a distance of N that'll get us to the place we need to go up to G. So if I go M minus N and then up a distance of R. M minus N and then up a distance of R. And I'm done but I can do a quick check. R and R up on top, zero and zero down below. And then remember these two values, these two X values should add up to this one. This is negative N plus M which is the same thing as M minus N M minus N and we're done.