1 00:00:00,000 --> 00:00:00,520 2 00:00:00,520 --> 00:00:03,730 What we're going to do in this video is, through a bunch of 3 00:00:03,730 --> 00:00:06,710 examples, familiarize ourselves with the 4 00:00:06,710 --> 00:00:07,669 x,y-coordinate plane. 5 00:00:07,669 --> 00:00:10,810 And first we're going to just look at some points that are 6 00:00:10,810 --> 00:00:13,500 already plotted and figure out their coordinates. 7 00:00:13,500 --> 00:00:15,390 Then we're going to look at some coordinates and figure 8 00:00:15,390 --> 00:00:16,289 out where those points are. 9 00:00:16,289 --> 00:00:17,394 Then we'll do one more problem. 10 00:00:17,394 --> 00:00:19,699 So let's figure out what are the 11 00:00:19,699 --> 00:00:21,890 coordinates of these points? 12 00:00:21,890 --> 00:00:24,550 So you have this point right here, A. 13 00:00:24,550 --> 00:00:26,679 So its x-coordinate, you can see it right there. 14 00:00:26,679 --> 00:00:27,600 You just drop down. 15 00:00:27,600 --> 00:00:29,800 Where does it intersect the x-axis? 16 00:00:29,800 --> 00:00:31,346 x is equal to 5. 17 00:00:31,346 --> 00:00:36,960 So it's the point 5 comma and y is going to be equal to 6. 18 00:00:36,960 --> 00:00:38,990 5 comma 6. 19 00:00:38,990 --> 00:00:41,920 Now this point B here, what's the x-coordinate? 20 00:00:41,920 --> 00:00:43,920 It is 5 to the left. 21 00:00:43,920 --> 00:00:45,940 5 to the left of the x-axis. 22 00:00:45,939 --> 00:00:47,495 This is negative 5. 23 00:00:47,496 --> 00:00:50,590 Its x-coordinate is negative 5. 24 00:00:50,590 --> 00:00:54,340 y-coordinate is, if you just go straight to the right, 25 00:00:54,340 --> 00:00:57,210 you're going to hit y is equal to 5. 26 00:00:57,210 --> 00:00:58,619 y is equal 5. 27 00:00:58,619 --> 00:01:00,189 Let me switch colors. 28 00:01:00,189 --> 00:01:01,049 C. 29 00:01:01,049 --> 00:01:02,750 I think you're getting the hang of this. 30 00:01:02,750 --> 00:01:06,040 Let's do the y-coordinate first. The y-coordinate is 3. 31 00:01:06,040 --> 00:01:07,760 You see that right there. 32 00:01:07,760 --> 00:01:10,440 And then the x-coordinate is negative 2. 33 00:01:10,439 --> 00:01:11,129 Negative 2. 34 00:01:11,129 --> 00:01:12,849 You always put the x-coordinate first. That's 35 00:01:12,849 --> 00:01:14,799 just the convention we use. 36 00:01:14,799 --> 00:01:18,659 D, x-coordinate negative 2. 37 00:01:18,659 --> 00:01:20,209 You see that right there. 38 00:01:20,209 --> 00:01:23,750 y-coordinate negative 2, as well. 39 00:01:23,750 --> 00:01:25,040 Let me get another color. 40 00:01:25,040 --> 00:01:28,170 E, let's do the y-coordinate. 41 00:01:28,170 --> 00:01:29,650 We'll figure it out first, but you always 42 00:01:29,650 --> 00:01:31,450 have to write it second. 43 00:01:31,450 --> 00:01:32,780 It's negative 4. 44 00:01:32,780 --> 00:01:34,510 You see that right there, the y-coordinate. 45 00:01:34,510 --> 00:01:37,420 The x-coordinate is 3. 46 00:01:37,420 --> 00:01:39,820 And then finally, F. 47 00:01:39,819 --> 00:01:42,045 The x-coordinate is 2. 48 00:01:42,046 --> 00:01:46,000 And the y-coordinate is negative 6. 49 00:01:46,000 --> 00:01:48,549 Hopefully that gives you a sense of at least figuring out 50 00:01:48,549 --> 00:01:49,569 the coordinates. 51 00:01:49,569 --> 00:01:50,549 Now let's go the other way. 52 00:01:50,549 --> 00:01:53,189 Let's start with coordinates and figure out where those 53 00:01:53,189 --> 00:01:54,599 points are. 54 00:01:54,599 --> 00:01:55,899 So you have this first one. 55 00:01:55,900 --> 00:01:58,560 I'll do it lowercase case a in parentheses to differentiate 56 00:01:58,560 --> 00:02:00,200 it from this uppercase A. 57 00:02:00,200 --> 00:02:03,189 So it's at 4 comma 2. x is equal to 4. 58 00:02:03,189 --> 00:02:04,500 y is equal to 2. 59 00:02:04,500 --> 00:02:08,409 60 00:02:08,409 --> 00:02:11,359 So that's that point right there. 61 00:02:11,360 --> 00:02:12,855 Let's do the next one. 62 00:02:12,854 --> 00:02:15,849 Let me do it in a color that you'll be able to read. 63 00:02:15,849 --> 00:02:17,150 b. 64 00:02:17,150 --> 00:02:20,680 x is equal to negative 3. 65 00:02:20,680 --> 00:02:23,189 y is equal to 5.5. 66 00:02:23,189 --> 00:02:27,479 So you go all the way up to 5.5. 67 00:02:27,479 --> 00:02:29,439 y is equal to 5.5. 68 00:02:29,439 --> 00:02:34,099 So that is the point lowercase b with parentheses around it. 69 00:02:34,099 --> 00:02:39,049 Then c, 4 negative 4. x is equal to 4. 70 00:02:39,050 --> 00:02:41,300 y is equal to negative 4. 71 00:02:41,300 --> 00:02:44,189 Right over there. 72 00:02:44,189 --> 00:02:45,609 And then one last one. 73 00:02:45,610 --> 00:02:47,230 I'll do it in orange. 74 00:02:47,229 --> 00:02:50,914 d, x is negative 2, y is negative 3. 75 00:02:50,914 --> 00:02:54,759 76 00:02:54,759 --> 00:02:56,139 Right there. 77 00:02:56,139 --> 00:02:58,179 That's the d with parentheses. 78 00:02:58,180 --> 00:02:58,980 And you could have gone the other way. 79 00:02:58,979 --> 00:03:01,789 You could have said, hey, y is equal to negative 3. 80 00:03:01,789 --> 00:03:02,689 x is equal to negative 2. 81 00:03:02,689 --> 00:03:04,359 So you could go to the left and down. 82 00:03:04,360 --> 00:03:06,070 Or you could go down and to the left. 83 00:03:06,069 --> 00:03:09,609 And you're still going to get to the same point. 84 00:03:09,610 --> 00:03:12,400 So hopefully that gives you a good sense of how to figure 85 00:03:12,400 --> 00:03:13,159 out coordinates. 86 00:03:13,159 --> 00:03:15,159 Or if you're given coordinates, how to figure out 87 00:03:15,159 --> 00:03:17,549 where to plot something on the x,y-coordinate plane. 88 00:03:17,550 --> 00:03:20,480 Now let's do a slightly more involved problem. 89 00:03:20,479 --> 00:03:24,099 So it says the following 3 points are 3 vertices of 90 00:03:24,099 --> 00:03:26,000 square A, B, C, D. 91 00:03:26,000 --> 00:03:27,439 Plot them on a graph. 92 00:03:27,439 --> 00:03:29,180 Then determine what the coordinates of the fourth 93 00:03:29,180 --> 00:03:31,030 point, D, would be. 94 00:03:31,030 --> 00:03:33,210 All right, let's plot these on a graph, as 95 00:03:33,210 --> 00:03:35,230 they tell us to do. 96 00:03:35,229 --> 00:03:35,859 All right. 97 00:03:35,860 --> 00:03:38,890 That'll be my y-axis. 98 00:03:38,889 --> 00:03:41,409 That's my y-axis. 99 00:03:41,409 --> 00:03:42,909 The vertical axis. 100 00:03:42,909 --> 00:03:44,159 That'll be my x-axis. 101 00:03:44,159 --> 00:03:46,620 102 00:03:46,620 --> 00:03:48,750 And let me put some-- let me mark it. 103 00:03:48,750 --> 00:03:52,800 So that's x equals 1, 2, 3, 4. 104 00:03:52,800 --> 00:03:56,700 This is x is equal to negative 1, negative 2, negative 3, 105 00:03:56,699 --> 00:03:57,459 negative 4. 106 00:03:57,460 --> 00:04:01,000 That's y is equal to 1, 2, 3, 4. 107 00:04:01,000 --> 00:04:04,270 This is y is equal to negative 1, negative 2, negative 3, 108 00:04:04,270 --> 00:04:05,590 negative 4. 109 00:04:05,590 --> 00:04:07,349 I could write that this y equals 4. 110 00:04:07,349 --> 00:04:10,530 This y equals negative 4. x is equal to 4. 111 00:04:10,530 --> 00:04:13,949 x is equal to negative 4. 112 00:04:13,949 --> 00:04:15,179 And let's see. 113 00:04:15,180 --> 00:04:16,649 Let's plot these points. 114 00:04:16,649 --> 00:04:18,970 So first, we have the point A is equal to negative 4, 115 00:04:18,970 --> 00:04:20,730 negative 4. 116 00:04:20,730 --> 00:04:23,230 So we go x is negative 4. 117 00:04:23,230 --> 00:04:24,810 And then y is negative 4. 118 00:04:24,810 --> 00:04:27,040 So we drop down 4 right there. 119 00:04:27,040 --> 00:04:29,790 And that is our point A. 120 00:04:29,790 --> 00:04:32,080 Negative 4, negative 4. 121 00:04:32,079 --> 00:04:34,349 And just to familiarize yourself with a labeling 122 00:04:34,350 --> 00:04:36,790 scheme that you may or may not have seen before, is that 123 00:04:36,790 --> 00:04:39,600 people label these sections of the coordinate plane. 124 00:04:39,600 --> 00:04:41,439 They call this the first quadrant. 125 00:04:41,439 --> 00:04:43,509 They call this the second quadrant. 126 00:04:43,509 --> 00:04:45,849 They call this the third quadrant. 127 00:04:45,850 --> 00:04:47,950 And they call this the fourth quadrant. 128 00:04:47,949 --> 00:04:51,289 And these are just the Roman numerals for I, II, III, and 129 00:04:51,290 --> 00:04:53,569 IV, So this point is in the third quadrant. 130 00:04:53,569 --> 00:04:56,480 When we looked up at this stuff over here, these points 131 00:04:56,480 --> 00:04:57,840 are in the fourth quadrant. 132 00:04:57,839 --> 00:05:01,159 These are in the third, second, first. Just an 133 00:05:01,160 --> 00:05:02,430 interesting thing to know. 134 00:05:02,430 --> 00:05:03,920 Sometimes someone might ask you, what quadrant 135 00:05:03,920 --> 00:05:04,540 is that point in? 136 00:05:04,540 --> 00:05:05,990 And you just say, OK, I see. 137 00:05:05,990 --> 00:05:08,850 If they're both negative, they're going to be in the 138 00:05:08,850 --> 00:05:10,000 third quadrant. 139 00:05:10,000 --> 00:05:13,100 If just the y is negative, but the x is positive, you're 140 00:05:13,100 --> 00:05:14,640 going to be in the fourth. 141 00:05:14,639 --> 00:05:17,560 If they're both positive, you're in the first. If y is 142 00:05:17,560 --> 00:05:19,759 positive, but x is negative, you're in the second. 143 00:05:19,759 --> 00:05:21,149 And we'll talk a little bit about that as 144 00:05:21,149 --> 00:05:22,479 we plot these points. 145 00:05:22,480 --> 00:05:24,879 So point B, x is positive. 146 00:05:24,879 --> 00:05:26,730 It's 1, 2, 3. 147 00:05:26,730 --> 00:05:28,430 And y is negative 4. 148 00:05:28,430 --> 00:05:31,709 So we drop down here into the fourth quadrant. 149 00:05:31,709 --> 00:05:33,579 That is the point B. 150 00:05:33,579 --> 00:05:35,620 It's 3, negative 4. 151 00:05:35,620 --> 00:05:38,280 So we can already see the bottom of our rectangle that 152 00:05:38,279 --> 00:05:39,919 they're talking about, right there. 153 00:05:39,920 --> 00:05:43,699 And notice, both of these have the exact same y. 154 00:05:43,699 --> 00:05:48,079 They're both at the same level below the x-axis. 155 00:05:48,079 --> 00:05:49,599 And then what's the next point? 156 00:05:49,600 --> 00:05:51,879 Point C is 3 comma 3. 157 00:05:51,879 --> 00:05:53,879 So 3 comma 3. 158 00:05:53,879 --> 00:05:55,100 It's in the first quadrant. 159 00:05:55,100 --> 00:05:57,600 Both of its coordinates are positive. 160 00:05:57,600 --> 00:05:58,490 3 comma 3. 161 00:05:58,490 --> 00:05:59,910 Both x and y are positive. 162 00:05:59,910 --> 00:06:02,620 And notice, it's on the same vertical as B. 163 00:06:02,620 --> 00:06:04,689 It has the same x value. 164 00:06:04,689 --> 00:06:06,459 They both have an x value of 3. 165 00:06:06,459 --> 00:06:08,219 So it's right above it. 166 00:06:08,220 --> 00:06:08,910 Right above it. 167 00:06:08,910 --> 00:06:12,210 Now we have to figure out the last point here. 168 00:06:12,209 --> 00:06:14,739 Well, the point is going to have to be on the same 169 00:06:14,740 --> 00:06:15,759 vertical as this point. 170 00:06:15,759 --> 00:06:17,689 It's going to have to be on the same vertical as this 171 00:06:17,689 --> 00:06:20,290 point, which means it's going to have the same x value as 172 00:06:20,290 --> 00:06:21,250 this point. 173 00:06:21,250 --> 00:06:24,319 So its x value is going to be negative 4. 174 00:06:24,319 --> 00:06:26,360 And then it's going to have to be on the same horizontal as 175 00:06:26,360 --> 00:06:27,660 this point. 176 00:06:27,660 --> 00:06:28,680 It's going to have to be on the same 177 00:06:28,680 --> 00:06:30,019 horizontal as that point. 178 00:06:30,019 --> 00:06:32,560 So it's going to have to have the same y value at the same 179 00:06:32,560 --> 00:06:34,319 height above the x-axis. 180 00:06:34,319 --> 00:06:36,269 So it's going to have to be 3. 181 00:06:36,269 --> 00:06:38,569 So that is our point D. 182 00:06:38,569 --> 00:06:41,849 Notice it's at negative 4, right above A. 183 00:06:41,850 --> 00:06:44,230 And it's at y is equal to 3. 184 00:06:44,230 --> 00:06:47,210 Right to the left of point C. 185 00:06:47,209 --> 00:06:48,979 And we are done. 186 00:06:48,980 --> 00:06:49,266