1 00:00:00,690 --> 00:00:07,710 Let's do this question, find the center of the triangle whose vertices are five comma for zero comma 2 00:00:07,710 --> 00:00:09,400 four and five, comma zero. 3 00:00:09,600 --> 00:00:13,330 All right, pause the video, give it a try and then let's do it together. 4 00:00:13,590 --> 00:00:14,040 All right. 5 00:00:14,040 --> 00:00:14,550 We are back. 6 00:00:14,700 --> 00:00:15,730 Let's do it together. 7 00:00:15,930 --> 00:00:21,450 Let me draw the axis over here and let me get started by plotting these three points. 8 00:00:21,750 --> 00:00:26,730 So this is zero comma for this is five comma four and this is five comma zero. 9 00:00:27,090 --> 00:00:30,060 Let me join these vertices to get the triangle. 10 00:00:30,460 --> 00:00:31,050 All right. 11 00:00:31,230 --> 00:00:35,310 Now, we need to first find the length of the sites right over here. 12 00:00:35,310 --> 00:00:37,020 You can see that this is a line. 13 00:00:37,230 --> 00:00:42,500 Where would this point and this point has the same Y coordinate. 14 00:00:42,510 --> 00:00:43,500 That's four and four. 15 00:00:43,500 --> 00:00:43,770 Right. 16 00:00:43,950 --> 00:00:46,730 So this line will be parallel to the X axis. 17 00:00:46,740 --> 00:00:51,260 So I just need to find the difference between the X coordinates to find this length. 18 00:00:51,420 --> 00:00:52,600 That's five minus zero. 19 00:00:52,770 --> 00:00:54,840 So this length over here is five units. 20 00:00:54,960 --> 00:00:58,650 And similarly, you can find that this length over here is four units, right. 21 00:00:58,680 --> 00:01:00,930 Because it has the same X coordinates. 22 00:01:01,080 --> 00:01:03,450 So this line is parallel to the Y axis. 23 00:01:03,690 --> 00:01:07,840 And I just need to do for minus zero to find this length over here. 24 00:01:08,100 --> 00:01:14,340 Now, after getting five over here and four over here, I can use Pythagoras Theorem right this length 25 00:01:14,340 --> 00:01:17,650 over here will be a square root of PI squared plus four square. 26 00:01:17,700 --> 00:01:19,250 That's equal to 41. 27 00:01:19,350 --> 00:01:19,560 Right. 28 00:01:19,650 --> 00:01:20,620 Root of 41. 29 00:01:20,880 --> 00:01:21,320 All right. 30 00:01:21,990 --> 00:01:26,640 Now, we have found the three sides of this triangle right now. 31 00:01:26,760 --> 00:01:29,080 Remember, how do we find the center? 32 00:01:29,280 --> 00:01:36,450 You need to multiply the length of the side with the corresponding coordinate of the opposite vertex. 33 00:01:36,450 --> 00:01:39,750 That is to find the X coordinate of this. 34 00:01:39,990 --> 00:01:45,170 In the center of this triangle, you need to multiply four with zero. 35 00:01:45,210 --> 00:01:48,450 Right, because over here you have zero four into zero. 36 00:01:48,480 --> 00:01:51,740 That's this year plus five in two. 37 00:01:52,890 --> 00:01:53,670 Sorry, this five. 38 00:01:53,670 --> 00:01:55,650 This five into this five. 39 00:01:55,650 --> 00:01:56,060 Right. 40 00:01:56,100 --> 00:01:57,180 So five to five. 41 00:01:57,180 --> 00:01:58,350 That's this over here. 42 00:01:58,710 --> 00:02:02,300 Plus root of 41 into this five over here. 43 00:02:02,310 --> 00:02:08,220 So root for into five divided by A plus B plus that's five plus four plus Route 41. 44 00:02:08,430 --> 00:02:14,520 Similarly to find the Y coordinate you need to multiply four with this, four over here. 45 00:02:14,520 --> 00:02:18,790 That's four in the four plus five into this zero over here. 46 00:02:18,810 --> 00:02:22,820 So five zero plus Route 41 into this four over here. 47 00:02:23,010 --> 00:02:27,600 And then you need to divide it with A plus B plus there's five plus four plus Route 41. 48 00:02:27,760 --> 00:02:29,030 And this is your answer. 49 00:02:29,190 --> 00:02:36,690 And this simplifies to twenty five plus five, Route 41 by nine plus Route 41, comma 16 plus four, 50 00:02:36,690 --> 00:02:40,400 Route 41 divided by nine plus Route 41. 51 00:02:40,410 --> 00:02:41,760 And that is your answer.