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Points on the coordinate plane examples

CCSS.Math: ,

Video transcript

what we're going to do in this video is through a bunch of examples familiarize ourselves with the XY coordinate plane and first we're going to just look at some points that are already plotted and figure out their coordinates then we're going to look at some coordinates and figure out where those points are and then we'll do one more problem so let's figure out what are the coordinates of these points so you have this point right here a so its x-coordinate you can see it right there you just drop down where does it intersect the x-axis X is equal to 5 so it's the point 5 comma and Y is going to be equal to 6 5 comma 6 now this point B here what's the x-coordinate it is 5 to the left 5 to the left of the x-axis this is negative 5 x axis x-coordinate is negative 5 y coordinate is if you just go straight to the right you're going to hit Y is equal to 5 y is equal to 5 let me switch colors see I think you're getting the hang of this let's do the y coordinate first the y coordinate is 3 you see that right there and then the x coordinate is negative 2 negative 2 you always put the x coordinate first that's just the convention we use the x coordinate negative 2 you see that right there y coordinate negative 2 as well let me get another color II the let's do the y coordinate well we'll figure it out first but you always have to write it second it's negative 4 you see that right there the y coordinate the x coordinate is 3 and then finally f the x coordinate is 2 and the y coordinate is negative 6 hopefully that gives you a sense of at least figuring out the coordinates now let's go the other way let's start with coordinates and figure out where those points are so you have this first one I'll do it lowercase a in parenthesis to differentiate it from this uppercase a so it's at 4 comma 2 X is equal to 4 y is equal to 2 X is equal to 4 y is equal to 2 so that's that point right there let's do the next one let me do it in a color that you'll be able to read B X is equal to negative three X is equal to negative three y is equal to five point five so you go all the way up to five point five right y is equal to five point five so that is the point lowercase B with parentheses around it then C for negative four X is equal to 4 y is equal to negative four right over there and then one last one I'll do it in orange D X is negative 2 y is negative three X is negative 2 y is negative three right there that's the D with parentheses and you could have gone the other way you can say hey y is equal to negative three X is equal to negative two so you could go to the left and down or you could go down into the left and you're still going to get to the same point so hopefully that gives you a good sense of how to figure out coordinates or if you're given coordinates how to figure out where to plot something on the XY coordinate plane now let's do a slightly more involved problem so it says the following three points are three vertices of square ABCD plot them on a graph then determine what the coordinates of the fourth point D would be all right let's plot these on a graph as they tell us to do all right that'll be my y-axis that's my y-axis the vertical axis that'll be my x-axis and let me put some let me mark it so that's x equals 1 2 3 4 this is X is equal to negative 1 negative 2 negative 3 negative 4 that's y is equal to 1 2 3 4 this is y is equal to negative 1 negative 2 negative 3 negative 4 I could write that this y equal 4 it's y equals negative 4 x is equal to 4 X is equal to negative 4 and see let's plot these points so first we have the point a is equal to negative 4 negative 4 so we go X is negative 4 and then Y is negative 4 so we drop down 4 right there and that is our point a negative four negative four and just to familiarize yourself with a labeling scheme that you may or may not have seen before is that people label these sections of the coordinate plane they call this the first quadrant they call this the second quadrant they call this the third quadrant and this is they call this the fourth quadrant and these are just the Roman numerals for one two three and four so this point is in the third quadrant when we looked up at this stuff over here these points are in the fourth quadrant these are in the third second first just a interesting thing to know sometimes someone might ask you what quadrant does that point in you just say oh okay I see if they're both negative they're going to be in the four in the third quadrant if just the Y is negative but the X is positive you're going to be in the fourth if they're both positive you're in the first if Y is positive but X is negative you're in the second and we'll talk a little bit about that as we plot these points so point be X is positive it's one two three and Y is negative four so we drop down here into the fourth quadrant that is the point B it's three negative four so we can already see the bottom of our rectangle that they're talking about right there and notice both of these have the exact same y they're both at the same level below the x-axis and then what's the next point Point C is 3 comma 3 so 3 comma 3 it's in the first quadrant both of its coordinates are positive 3 comma 3 both x and y are positive and notice it's on the same vertical as B it has the same x value they both have an x value of 3 so it's right above it right above it now we have to figure out the last point here well the point is going to have to be on the same vertical as this point it's going to have to be on the same vertical as this point which means it's going to have to have the same x value as this point so the x value is going to be negative 4 and then it's going to have to be on the same horizontal as this point it's going to have to be on the same horizontal as that point so it's going to have to have the same y value it's at the same height above the x-axis so it's going to have to be 3 so that is our point d notice it's that negative 4 right above a and it's at Y is equal to three right to the left of point C and we are done