1 00:00:00,620 --> 00:00:06,530 Let's do this question, the image of point three, comma five by the line of symmetry, which is equal 2 00:00:06,530 --> 00:00:08,420 to one by two is the point. 3 00:00:08,420 --> 00:00:10,730 C, find the coordinates of C. 4 00:00:11,060 --> 00:00:11,480 All right. 5 00:00:11,480 --> 00:00:14,480 Pause the video, give it a try and then let's do it together. 6 00:00:14,900 --> 00:00:15,320 All right. 7 00:00:15,320 --> 00:00:15,750 We're back. 8 00:00:15,770 --> 00:00:17,490 Let's do it together over here. 9 00:00:17,660 --> 00:00:22,310 Why is equal to one by two X and it's nine, which we have not yet discussed. 10 00:00:22,490 --> 00:00:24,320 So this is part of the general case. 11 00:00:24,590 --> 00:00:29,660 Let me draw my axis over here and let me plot three comma five over here. 12 00:00:29,990 --> 00:00:33,200 Now, this is the nine Y is equal to one by two X.. 13 00:00:33,500 --> 00:00:37,940 Now, I need to find the reflection of this point about this line. 14 00:00:38,210 --> 00:00:45,080 That means I need to draw a line which is perpendicular to Y is equal to one by two X and it passes 15 00:00:45,080 --> 00:00:46,510 through three comma five. 16 00:00:47,150 --> 00:00:54,820 And after this, I need to find a point on this line which is equidistant from this line right as the 17 00:00:54,820 --> 00:00:56,340 distance of this point from this line. 18 00:00:56,600 --> 00:01:01,030 Now this line over here will be Y is equal to minus two explicit. 19 00:01:01,220 --> 00:01:02,140 Can you tell me why? 20 00:01:02,360 --> 00:01:04,970 Because over here the slope is one by two. 21 00:01:04,970 --> 00:01:05,300 Right. 22 00:01:05,550 --> 00:01:11,510 Therefore, the slope over here has to be minus two because these two have to be perpendicular and one 23 00:01:11,510 --> 00:01:13,850 by two in the minus two gives me minus one. 24 00:01:14,090 --> 00:01:18,580 Right now, this line passes through this point over here. 25 00:01:18,590 --> 00:01:18,890 Right. 26 00:01:19,070 --> 00:01:25,610 So let me substitute this point into this line that gives me five into five is equal to minus two in 27 00:01:25,610 --> 00:01:28,810 the three, plus C or C is equal to eleven. 28 00:01:29,380 --> 00:01:29,920 All right. 29 00:01:30,110 --> 00:01:36,110 Now, that means this line over here is why is equal to minus two X plus 11. 30 00:01:36,470 --> 00:01:36,940 All right. 31 00:01:37,130 --> 00:01:43,880 Now, let me substitute Y is equal to one by two X into this equation, because these two lines are 32 00:01:43,880 --> 00:01:45,500 intersecting at this point. 33 00:01:45,620 --> 00:01:47,570 And I'm trying to find out this point. 34 00:01:47,600 --> 00:01:53,030 OK, so one by two X is equal to minus two X plus 11 or five by two. 35 00:01:53,030 --> 00:01:54,230 X is equal to 11. 36 00:01:54,560 --> 00:01:57,320 And that gives me X is equal to 22 by five. 37 00:01:57,650 --> 00:02:00,110 Now we know why is equal to one by two X. 38 00:02:00,350 --> 00:02:04,970 So if X is equal to twenty two by five, Y will be eleven by five. 39 00:02:05,600 --> 00:02:05,960 Right. 40 00:02:06,350 --> 00:02:06,790 All right. 41 00:02:06,920 --> 00:02:08,530 So that is this point over here. 42 00:02:08,690 --> 00:02:10,520 That's twenty two by five comma. 43 00:02:10,520 --> 00:02:11,490 Eleven by five. 44 00:02:11,750 --> 00:02:14,720 Now let this point C be equal maybe. 45 00:02:15,700 --> 00:02:22,690 Now, this point is the reflection of a about this line, right, that means the distance, Abe. 46 00:02:23,890 --> 00:02:31,510 Has to be equal to the distance C or it means that B is the midpoint of nine segment AC. 47 00:02:31,620 --> 00:02:31,960 Right. 48 00:02:32,860 --> 00:02:40,450 OK, let me make some space over here, if by the midpoint of AC, that means a plus three by two should 49 00:02:40,450 --> 00:02:42,220 give me 22 by five, right. 50 00:02:43,440 --> 00:02:49,700 OK, so that means is equal to forty four by five, minus three, which is equal to twenty nine by five, 51 00:02:49,980 --> 00:02:54,980 similarly B plus five by two should be equal to eleven by five. 52 00:02:55,260 --> 00:03:01,770 That is basically twenty two by five minus five, or that's equal to minus three by five. 53 00:03:02,190 --> 00:03:10,140 And hence the answer that is the coordinates of point C is twenty nine by five comma minus three by 54 00:03:10,140 --> 00:03:10,650 five.