Distance Polygons on the Coordinate Plane

good morning i'm going to try to make this as fast as possible today we talked about distance in polygons on the coordinate plane this is topic 24 in your notebook so you will turn to your table of contents right 24 and then write this title down i'm going to make it quick so feel free to pause and replay as many times as you feel like you need to so today our main focus was on using absolute value to find the distance between points like number one to find the distance between point and without counting because sometimes we don't have the coordinate plane we're going to use their coordinates which point is at 3 2 and he's in quadrant 1 and point is at 3 negative 3 and he's in quadrant 4. so the first thing we do is we look and see which one of their values differs does their differ or they're different and in this case it looks like their values differ so i'm going to highlight those so when they're in different quadrants like this we are going to be adding their absolute values so i'm going to take the absolute value of 2 and add it to the absolute value of negative 3 to get total distance of 5 units now if wanted to double check myself could just take my pencil and go from to because do actually have this grid one two three four five checks out five units apart number two says what is the distance between points and well we just use point so i'm going to rewrite him just like he is in quadrant one then i'm going to find point he's down here in quadrant four and he is an ordered pair 3 negative 5. so again need to find which one of their values x's or y's differ and it looks like the values and if you'll notice look they are vertically distance apart just like the y-axis is vertical so i'm going to circle their y-values then i'm going to take the absolute value of negative 5 i'm going to add the absolute value of 2 and five plus two gives me seven there are seven units apart and could keep going and wouldn't that in fact find five plus two is seven on number three am looking for the distance between points which just did three negative five in quadrant four and point this is new one he's way over here in quadrant three and he is at negative one negative five so on this one it looks like their values are different and look at this they are horizontally separated so their values are three and negative and since they're in different quadrants again i'm going to add their absolute values when they are in different quadrants you add their absolute values and 3 plus 1 makes 4. four units number four is little more tricky because they are asking which of these points or is four units from this guy which i'm going to plot negative 1 negative 3 and this graph's hard to see so you may want to draw your little lines or definitely count down and 2 units away from 3 negative 1. so that's over here and the only point that qualifies to be four away from this guy three four and two away from this guy is point so he's the only one that qualifies all right now let's look at the bottom half of the paper on the bottom half it says draw the polygon with given vertices and we've actually drawn this before if you did notes from friday then you have this so to draw this polygon we've got to go right 4 up 4 for point so plot him and label him then right 7 and up 4 for point write 7 up 1 for and right 4 up 1 for and we are drawing polygon so let's connect them then it's asking me what is the distance between points and well did you notice this entire shape is in quadrant one they're all in the same quadrant so do want to go back to my points and look the only ones that differ are their values when they're in the same quadrant you find their difference so when they're in the same quadrant you're finding the difference between them so you're subtracting i'm going to make little side note and i'm going to say same i'm going to abbreviate quad for quadrant subtract only when they're in the same one because don't have to go to my axis to get on the other side so 7 minus 4 does give me 3 units there's 3 units between point and point three what type of polygon is this can look at it and clearly see this guy is rectangle but he's just more than rectangle he could also be quadrilateral great spelling word by the way or he has three by three so he could be square then finally what is the area of the shape if you recall area is the number of square units it takes to cover the space you will need to know this for that mr mcdunk paper it's called get moving so would have to take the length and multiply it by the width remember the dot means times so if it's by 3 then it gives me an area of 9 9 square units so once you're finished taking your notes go ahead and trim and paste this in your notebook then you are to complete that mr mcdunk paper that assigned on google classroom be sure and read it very very carefully all right have great day