1 00:00:00,550 --> 00:00:04,900 High students, welcome to this section where we deal with Kornet geometry. 2 00:00:05,170 --> 00:00:06,160 Let's get started. 3 00:00:06,490 --> 00:00:10,390 Imagine that you have a piece of paper over here, right? 4 00:00:10,570 --> 00:00:12,730 And there is a dot on the paper. 5 00:00:13,000 --> 00:00:16,300 And you want to describe to somebody where the dot is. 6 00:00:16,570 --> 00:00:20,960 Now, if you tell that person this dot is five centimeters from the bottom. 7 00:00:21,190 --> 00:00:23,120 Is that enough to describe the dot? 8 00:00:23,320 --> 00:00:23,570 No. 9 00:00:23,600 --> 00:00:23,950 Right. 10 00:00:24,050 --> 00:00:29,820 Because you could have a point over here also or a point over here also that satisfies the given condition. 11 00:00:30,010 --> 00:00:37,030 But if you tell the person it's five centimeters from the bottom of the paper and it is 12 centimeter 12 00:00:37,240 --> 00:00:44,400 from the left border of the paper, then you can uniquely identify where the dot is located. 13 00:00:44,620 --> 00:00:44,940 Right. 14 00:00:45,160 --> 00:00:52,790 So that means we need two independent informations for finding the position of the dot right now. 15 00:00:52,900 --> 00:00:59,710 This is the concept behind the Cartesian system, right where we describe the position of a point in 16 00:00:59,710 --> 00:01:00,190 a plane. 17 00:01:00,430 --> 00:01:04,500 Now there is corner geometry, even for three dimensional geometry. 18 00:01:04,750 --> 00:01:09,430 But in this section, we only deal with two dimensional coordinate geometry. 19 00:01:09,670 --> 00:01:10,090 All right. 20 00:01:10,270 --> 00:01:13,990 Now let's try to understand what the Cartesian system is. 21 00:01:14,380 --> 00:01:20,920 Now, over here we have two axis and they are placed perpendicular to one another. 22 00:01:21,430 --> 00:01:26,630 Now, that's why this angle over here is 90 and let them intersect at point all. 23 00:01:26,830 --> 00:01:28,990 And we call this point the origin. 24 00:01:29,410 --> 00:01:33,580 Now, this axis over here is called the x axis. 25 00:01:35,220 --> 00:01:39,540 All right, and this Axe's over here is called the Y-axis. 26 00:01:41,240 --> 00:01:48,050 All right, now I have I put measurements on this in such a way that whatever is on this side is the 27 00:01:48,050 --> 00:01:54,050 positive value for the x axis values, and this side will have the negative values for the X axis. 28 00:01:54,380 --> 00:02:00,650 Similarly, this up over here is the positive Y axis and this is the negative y axis. 29 00:02:00,920 --> 00:02:01,370 All right. 30 00:02:01,520 --> 00:02:05,080 Now let's plot a few points to see how this actually works. 31 00:02:07,580 --> 00:02:13,610 All right, so I have plotted a few points over here, you can see that you have one over here to over 32 00:02:13,610 --> 00:02:16,840 here, three over here, and it keeps going on like this. 33 00:02:17,120 --> 00:02:22,660 Now, over here, the negative axis, you have minus one, minus two, minus three, etc.. 34 00:02:22,910 --> 00:02:28,700 Now, remember, the distance between these two will be the same, and that's the same distance over 35 00:02:28,700 --> 00:02:30,300 here as well as over here. 36 00:02:30,320 --> 00:02:32,590 So it's one unit distance, right. 37 00:02:32,780 --> 00:02:35,090 And that same distance is maintained across. 38 00:02:35,320 --> 00:02:37,970 But even here also, you will have one unit distance. 39 00:02:41,630 --> 00:02:44,000 All right, now let's proceed. 40 00:02:44,210 --> 00:02:48,640 Now you can see that we call this x axis and y axis, right? 41 00:02:48,650 --> 00:02:51,050 That axis is the word that we used. 42 00:02:51,320 --> 00:02:54,620 Now, if you take them together, it's called axis. 43 00:02:54,650 --> 00:02:56,750 That's the plural way of writing axis. 44 00:02:57,230 --> 00:03:01,290 Now you can see that these two axis divides the plane. 45 00:03:01,310 --> 00:03:02,320 This is the plane, right? 46 00:03:02,380 --> 00:03:04,810 This is the plane plane surface. 47 00:03:05,390 --> 00:03:11,590 It divided this plane into four parts and we call these parts quadrants. 48 00:03:12,020 --> 00:03:16,540 So therefore, quadrants are one, two, three and four. 49 00:03:16,910 --> 00:03:23,270 You can see that in the first quadrant, anything located in the first quadrant as opposed to x axis 50 00:03:23,270 --> 00:03:25,950 value and the positive y axis value. 51 00:03:26,240 --> 00:03:29,430 Now, soon we will plot points and this will become more clear. 52 00:03:29,660 --> 00:03:32,240 But over here, you can see that X is negative. 53 00:03:32,390 --> 00:03:34,610 But why is positive all here? 54 00:03:34,700 --> 00:03:37,250 Why is negative and X is negative. 55 00:03:37,400 --> 00:03:42,200 And in the fourth quarter you can see that X is positive and Y is negative. 56 00:03:42,440 --> 00:03:42,880 All right. 57 00:03:43,130 --> 00:03:51,080 Now the plane is called also the Cartesian plane or the coordinate plane or the X Y plane and the X 58 00:03:51,080 --> 00:03:54,360 and Y axis are called the coordinate axis. 59 00:03:55,130 --> 00:04:00,830 Let's plot some points and analyze them to understand the x y plane in a better manner. 60 00:04:01,250 --> 00:04:01,700 All right. 61 00:04:01,820 --> 00:04:04,890 Over here we have point B and this is Point Cube. 62 00:04:05,300 --> 00:04:08,060 Now, what is the X coordinate of point B? 63 00:04:08,300 --> 00:04:12,610 You will see that the X coordinate of point B is equal to two. 64 00:04:12,950 --> 00:04:14,570 What is this to these two? 65 00:04:14,570 --> 00:04:22,940 Is this distance that is it's the perpendicular distance from the Y axis measured along the x axis. 66 00:04:22,940 --> 00:04:23,250 Right. 67 00:04:23,550 --> 00:04:29,120 Or to get two point two from y axis, you need to move two units. 68 00:04:29,490 --> 00:04:35,030 Similarly, the Y coordinate of point B will be one unit right now. 69 00:04:35,120 --> 00:04:38,450 The X coordinate is also called the APSA. 70 00:04:39,830 --> 00:04:45,590 And we have seen that the Y coordinate over here is one, right, because you need to move one unit 71 00:04:45,980 --> 00:04:52,370 from the X axis to get to point B, and this over here is also called the ordinate. 72 00:04:54,040 --> 00:05:02,080 All right, now we have checked point B, we have seen what the APSA and Ordinate is now to call point 73 00:05:02,080 --> 00:05:05,740 B or to the point B, we say P to one. 74 00:05:06,190 --> 00:05:13,540 That means this point B is two units from the Y axis or the X coordinate is two and the Y coordinate 75 00:05:13,540 --> 00:05:14,200 is one. 76 00:05:14,560 --> 00:05:14,990 All right. 77 00:05:15,100 --> 00:05:16,360 Now what about point? 78 00:05:16,360 --> 00:05:18,310 Q You will see that point. 79 00:05:18,310 --> 00:05:22,000 Q is three units along this axis, right? 80 00:05:22,390 --> 00:05:25,260 And it is one unit along this axis. 81 00:05:25,570 --> 00:05:31,510 So the X coordinate, four point two is minus three and the Y coordinate is minus one. 82 00:05:31,690 --> 00:05:34,870 Therefore we are right to minus three. 83 00:05:34,870 --> 00:05:35,600 Minus one. 84 00:05:36,400 --> 00:05:40,480 Let's plot some points to solidify our learning so far. 85 00:05:40,870 --> 00:05:41,370 All right. 86 00:05:41,500 --> 00:05:43,340 I have four points over here. 87 00:05:43,750 --> 00:05:45,490 Now, let's start with point A.. 88 00:05:45,880 --> 00:05:51,310 Now, over here you can see that the X coordinate of point is minus three, right? 89 00:05:51,580 --> 00:05:54,610 So I need to move three units still here. 90 00:05:54,820 --> 00:05:55,200 Right. 91 00:05:55,480 --> 00:05:57,730 And the Y coordinate is four. 92 00:05:57,850 --> 00:06:00,840 So I need to move four units along this axis. 93 00:06:00,850 --> 00:06:03,130 So that's one, two, three and four. 94 00:06:03,460 --> 00:06:10,120 Now, these two will meet over here and this is point eight and point is minus three. 95 00:06:10,300 --> 00:06:11,280 All right. 96 00:06:11,550 --> 00:06:11,960 All right. 97 00:06:12,200 --> 00:06:13,660 Now, what about point B? 98 00:06:13,930 --> 00:06:15,820 The X coordinate is minus two. 99 00:06:15,880 --> 00:06:19,950 So I need to travel down here and the Y coordinate is minus two. 100 00:06:19,960 --> 00:06:23,670 So I need to travel here and they need around over here. 101 00:06:23,680 --> 00:06:23,920 Right. 102 00:06:23,950 --> 00:06:25,580 So this is point B. 103 00:06:26,110 --> 00:06:27,930 Now what about point C? 104 00:06:28,210 --> 00:06:32,770 It has a zero X coordinate for the X coordinated zero at this point. 105 00:06:32,780 --> 00:06:36,190 Right now the Y coordinate is three point five. 106 00:06:36,220 --> 00:06:40,870 So that's one, two, three and three point five will be in between three and four. 107 00:06:40,870 --> 00:06:41,140 Right. 108 00:06:41,380 --> 00:06:43,620 Therefore, point C is over here. 109 00:06:43,900 --> 00:06:46,500 That's zero three point five. 110 00:06:46,510 --> 00:06:46,800 Right. 111 00:06:47,170 --> 00:06:48,550 What about point B? 112 00:06:48,820 --> 00:06:55,540 Point B is six point five zero to the X coordinate is six point five to let me travel six point five 113 00:06:55,540 --> 00:06:56,830 units in this direction. 114 00:06:57,070 --> 00:06:58,360 I reach about here. 115 00:06:58,420 --> 00:06:58,780 Right. 116 00:06:58,990 --> 00:07:02,700 And the Y coordinate is zero to that's over here itself. 117 00:07:02,890 --> 00:07:04,540 Therefore point these over here. 118 00:07:04,810 --> 00:07:06,910 This is six point five zero.