1 00:00:00,050 --> 00:00:02,010 Problem 38. 2 00:00:02,010 --> 00:00:03,230 In the drawing below, 3 00:00:03,230 --> 00:00:05,930 the figure formed by the squares with sides 4 00:00:05,930 --> 00:00:09,260 that are labeled x, y, and z is a right triangle. 5 00:00:09,260 --> 00:00:14,360 So the figure, so it's a right triangle. 6 00:00:14,360 --> 00:00:15,160 And then they ask us, 7 00:00:15,160 --> 00:00:19,030 which equation is true for all values of x, y, and z? 8 00:00:19,030 --> 00:00:21,000 So really, they're just trying to see 9 00:00:21,000 --> 00:00:29,900 if you remember the Pythagorean Theorem. 10 00:00:31,000 --> 00:00:33,890 And that just tells us that if we have a right triangle, 11 00:00:33,890 --> 00:00:39,390 that the sum of the squares of the two smaller sides, 12 00:00:39,390 --> 00:00:42,350 so x squared plus y squared, 13 00:00:42,350 --> 00:00:46,030 is going to be equal to the square of the longest side, 14 00:00:46,030 --> 00:00:49,000 or the side that's opposite the right angle. 15 00:00:49,000 --> 00:00:50,020 Or we also call that the hypotenuse. 16 00:00:53,050 --> 00:00:55,810 So that's equal to z squared. 17 00:00:55,810 --> 00:00:58,040 That's what the Pythagorean Theorem tells us. 18 00:00:58,040 --> 00:01:00,250 And so if we look down here, 19 00:01:00,250 --> 00:01:02,710 only one of those match what I just wrote down, 20 00:01:02,710 --> 00:01:06,000 are kind of my restatement of the Pythagorean Theorem. 21 00:01:06,000 --> 00:01:09,050 x squared plus y squared is equal to z squared. 22 00:01:09,050 --> 00:01:13,030 And that's this one right there, choice B. 23 00:01:13,030 --> 00:01:15,000 Next problem. 24 00:01:15,000 --> 00:01:18,020 Problem 39. 25 00:01:18,020 --> 00:01:22,030 A clothing company created the following diagram for a vest. 26 00:01:22,030 --> 00:01:24,760 So I guess this is somehow a vest. 27 00:01:24,760 --> 00:01:26,040 Maybe it's half of the vest, 28 00:01:26,040 --> 00:01:28,710 because I don't see how I could put that on me. 29 00:01:28,710 --> 00:01:30,520 To show the other side of the vest-- 30 00:01:30,520 --> 00:01:33,970 OK, right, so this was half of the vest-- 31 00:01:33,970 --> 00:01:41,060 the company will reflect the drawing across the y-axis. 32 00:01:41,060 --> 00:01:45,020 What will be the coordinates of C after the reflection? 33 00:01:45,020 --> 00:01:46,480 So when they say reflection, they mean, 34 00:01:46,480 --> 00:01:48,560 literally, just take the image of this 35 00:01:48,560 --> 00:01:50,800 and you flip it over onto the right-hand side. 36 00:01:50,800 --> 00:01:53,020 So I could draw it out, and draw it in blue. 37 00:01:53,020 --> 00:01:54,620 So if I take the reflection, 38 00:01:54,620 --> 00:01:57,020 this line right here is at negative 1. 39 00:01:57,020 --> 00:02:00,320 It's 1 to the left of the y-axis. 40 00:02:00,320 --> 00:02:03,950 So when I take its reflection, I would draw it right here, 41 00:02:03,950 --> 00:02:07,050 1 to the right of the y-axis. 42 00:02:07,050 --> 00:02:09,180 This line down here, 43 00:02:09,190 --> 00:02:15,010 it goes from 1 to the left all the way to 4 to the left. 44 00:02:15,010 --> 00:02:16,670 On this side, it's going to go from 1 to 45 00:02:16,670 --> 00:02:20,060 the right all the way to 4 to the right. 46 00:02:20,060 --> 00:02:22,040 I could keep doing it. 47 00:02:22,040 --> 00:02:25,660 This segment right here, FE, when I flip it, 48 00:02:25,660 --> 00:02:28,080 will become this segment right here. 49 00:02:28,080 --> 00:02:32,030 This segment, DE, right here, 50 00:02:32,030 --> 00:02:34,650 will become this segment. 51 00:02:34,650 --> 00:02:38,010 It'll just look something like this when I go onto that side 52 00:02:38,010 --> 00:02:43,020 And then C, right here, is 2 to the left of the y-axis. 53 00:02:43,020 --> 00:02:46,070 So C over here will be 2 to the right of the y-axis. 54 00:02:46,070 --> 00:02:48,410 So it's going to look something like this. 55 00:02:48,410 --> 00:02:52,010 So the vest is going to look something like this. 56 00:02:52,010 --> 00:02:54,000 And then of course, it just dips down like that. 57 00:02:54,000 --> 00:02:56,020 So that's the right-hand side of the vest. 58 00:02:56,020 --> 00:02:58,020 But they want to know what are the coordinates of C? 59 00:02:58,020 --> 00:03:01,240 So this is C, and this is the C after the reflection. 60 00:03:01,240 --> 00:03:03,010 Maybe I could call it C prime. 61 00:03:03,010 --> 00:03:07,040 And so its coordinates are-- its x-coordinate is 2. 62 00:03:07,040 --> 00:03:08,420 And we're 2 to the right; 63 00:03:08,420 --> 00:03:10,690 before, we were 2 to the left, at minus 2. 64 00:03:10,690 --> 00:03:13,260 And its y-coordinate is going to be the same, 65 00:03:13,260 --> 00:03:14,430 it's going to be 7. 66 00:03:14,430 --> 00:03:16,030 2, 7. 67 00:03:16,030 --> 00:03:18,000 So that is choice A. 68 00:03:21,060 --> 00:03:22,920 I'll do it in the next video. 69 00:03:22,920 --> 00:03:24,890 Well, there's only two problems in this video. 70 00:03:24,890 --> 00:03:26,740 So let me go to the next page. 71 00:03:30,060 --> 00:03:31,080 Number 40. 72 00:03:31,080 --> 00:03:34,260 What is the area, in square units, 73 00:03:34,260 --> 00:03:38,880 of trapezoid QRST shown below? 74 00:03:38,880 --> 00:03:40,320 So we need to figure out the area of this. 75 00:03:40,320 --> 00:03:42,010 And they actually even give us a formula. 76 00:03:42,010 --> 00:03:46,000 They gave us the formula for this trapezoid. 77 00:03:46,000 --> 00:03:50,770 So they're calling it 1/2 times the height, 78 00:03:50,780 --> 00:03:54,010 times base 1 plus base 2. 79 00:03:54,010 --> 00:03:55,600 So essentially, just to give you an intuition of 80 00:03:55,600 --> 00:03:57,710 where this comes from, you're essentially saying, 81 00:03:57,710 --> 00:04:00,030 what's the average width of this trapezoid? 82 00:04:00,030 --> 00:04:05,260 So you take 1/2 times the sum of this guy and that guy, 83 00:04:05,260 --> 00:04:06,620 and that gives you the average width. 84 00:04:06,620 --> 00:04:08,790 And then you multiply that times the height. 85 00:04:08,790 --> 00:04:11,610 So just applying this formula, 86 00:04:11,610 --> 00:04:16,430 it is 1/2 times my height-- my height is 8-- 87 00:04:16,430 --> 00:04:21,050 times base 1, let's call this base 1, 20. 88 00:04:21,050 --> 00:04:23,030 Plus base 2. 89 00:04:23,030 --> 00:04:25,570 Base 2 is this 6 right there. 90 00:04:25,570 --> 00:04:30,010 So I have 1/2 times 8, which is 4, times 26. 91 00:04:30,010 --> 00:04:36,000 And 4 times 26 is equal to 104 square units. 92 00:04:36,000 --> 00:04:37,230 So that's that right there. 93 00:04:37,230 --> 00:04:38,330 So they're really just testing 94 00:04:38,330 --> 00:04:39,770 whether you can apply this formula. 95 00:04:39,770 --> 00:04:41,370 Whether you can recognize what's the height 96 00:04:41,370 --> 00:04:44,070 and what are the two bases. 97 00:04:44,070 --> 00:04:46,020 Problem 41. 98 00:04:46,020 --> 00:04:47,260 One millimeter is. 99 00:04:47,260 --> 00:04:52,040 Well, here they're just seeing if you remember your units. 100 00:04:52,040 --> 00:04:53,360 Let me write it this way. 101 00:04:53,360 --> 00:04:57,050 Deci is equal to 1/10. 102 00:04:57,050 --> 00:05:01,400 Centi is equal to 1/100. 103 00:05:01,400 --> 00:05:10,000 And then milli is equal to 1/1000. 104 00:05:10,000 --> 00:05:15,010 So one millimeter is 1/1000 of a meter. 105 00:05:15,010 --> 00:05:19,070 They're just making sure you remember your metric prefixes. 106 00:05:19,070 --> 00:05:23,000 Problem 42. 107 00:05:23,000 --> 00:05:30,060 In the diagram below, hexagon LMNPQR is 108 00:05:30,060 --> 00:05:37,630 congruent to hexagon STUVWX. 109 00:05:37,630 --> 00:05:40,500 Congruent just means all the sides are equal 110 00:05:40,500 --> 00:05:43,480 and all the measures of their angles are also equal. 111 00:05:43,480 --> 00:05:50,580 So they say, which side is the same length as MN? 112 00:05:50,580 --> 00:05:52,410 So this is MN right there, and we want to know 113 00:05:52,410 --> 00:05:54,280 what side is the same length as that. 114 00:05:54,280 --> 00:05:58,000 So let me make sure that they're not trying to confuse us. 115 00:05:58,000 --> 00:06:04,260 So they start here, they say LMNPQR, 116 00:06:04,260 --> 00:06:09,000 and then they say STUVWX. 117 00:06:09,000 --> 00:06:10,000 So they're not confusing us. 118 00:06:10,000 --> 00:06:11,520 These points do correspond. 119 00:06:11,520 --> 00:06:13,660 S corresponds to L, M corresponds to T, 120 00:06:13,660 --> 00:06:15,030 and so forth and so on. 121 00:06:15,030 --> 00:06:18,270 So this segment is going to be congruent to 122 00:06:18,270 --> 00:06:19,430 that segment right there. 123 00:06:19,440 --> 00:06:21,570 Segment TU. 124 00:06:21,570 --> 00:06:24,530 So MN is the same length as TU. 125 00:06:25,000 --> 00:06:27,190 That is choice B.