draw-a-segment-overlinea-b-construct-a-segment-overlinex-y-whose-length-equals-frac34-a-b

Name: draw a segment overlinea b construct a segment overlinex y whose length equals frac34 a b
Uploaded: 2020-08-24
Duration: 57 s
Channel: Numerade
Description: Draw a segment $\overline{A B}$ . Construct a segment $\overline{X Y}$ whose length equals $\frac{3}{4} A B$ .

Question

Draw a segment $\overline{A B}$ . Construct a segment $\overline{X Y}$ whose length equals $\frac{3}{4} A B$ .

Ian Shi · Accepted Answer

all right, it&#x27;s going to be constructing United seven. That&#x27;s three quarters the length of a B to do this. Recommended buying this into two permanent court by sectors. So it&#x27;s over the compass. Maybe we&#x27;ll per particularly bisect. This were just bisected. Doesn&#x27;t happy Particular was gonna find the point that it goes through. It&#x27;s a little dryer. Curves like So get our bisecting point. That wasn&#x27;t really good drawn, very quality line. There we go. That&#x27;s bisected, and I will do it again. Same process. But for this point just did and be do, uh, glad down. And there&#x27;s our second bisected put. So without saying, is that this distance right over here three force, maybe.

Amrita Bhasin · Answer

okay. We know that BC is the square root of three s. Now that we&#x27;re looking at this, we know that a B squared plus C squared is BC squared. Therefore, we can draw our triangle. We know we have a 90 degree angle. We know this is us. This is squirt of to ask therefore this a squirt of three us.

Steven Swee · Answer

So this problem, Um, we need to draw a three inch line segments in divine line segment in such a way that we have a 1 to 4 segments ratio. And their instructions air page 40 47 of the textbook, which you could follow, and I will model those instructions on another slide. But you really try to figure out why. Does did instructions on page one or 47 work, right? So we can first start off with the 14 2nd ratio, right? Why do you have this one for segment ratio here? And Han, Do I follow the instructions in such a way that I get this ratio? Well, only that we can get one for second ratio. Let&#x27;s say I have a line segment here, right? So it starts a 0.1 and starts to some other ends at some other point. If I divide this line into five equal partitions So 12345 vehicle partitions because they are equal to one another. Get how One partition here. This of four partitions over here, right? This is for. And don&#x27;t give me this one of four second ratio here because each partition is equal to one another. So 123456 What matters is that is that I have five partitions. So if we can get our line segment to divide into on five vehicle partitions, then we really clear on where to place our point such that we had this one for segment ratio. Now one thing you easily do is take a three inch measurement trench line here and you&#x27;re three inches to our five and, um, find that one of force every racial very easily there. So we&#x27;re going to restrict use of ruler with you, Um, for just measuring a three inch line segment. So how do we do this here? Let&#x27;s say I have I Sorry, appoint a and that point a goes all the way to point. Hey won&#x27;t be, Honestly, this is the Rangers. I know it&#x27;s not three inches on the screen, but let&#x27;s just say it&#x27;s three inches. You&#x27;re right. It&#x27;s really hard to Randall through interest. Years will be pretty small and difficult to see. Let&#x27;s make a ray. Yeah, that starts a and just goes in some direction, right? And it so happens to pass a point C as such. The next thing we need to do here is determine how many are kissing to make in order to have those five equal partitions there. So let&#x27;s say here all right, I have my compass. I says some rates would be Any radius here has long since within, um, agency. Okay, so how one Dre here? I know this here. If I have this first, our cure, that&#x27;ll create one partition. So every are concrete. I use our treat. I add one more partition. So I want five arks here tackles five partitions here. So we have this even, um distribution or even partitions. And we can easily find that one of four second ratio. So let&#x27;s say I draw my five arks and they have to be all equal length equal in distance here when, when they intersect the racy. So let&#x27;s say five marks looked something like this was not perfect, but And she&#x27;ll be good enough representation here. So the intersect the point in a sector rate. At some point here, the next thing we need to do is take a last start here and draw a line from that last arc all the way to be okay. And, um, from this last Arkin, we need to copy this angle here after, Let&#x27;s call this point D We need a copy angle D a b using a compass or use our compass here. It looks like this here. It&#x27;s a really terrible looking couples. Looks more like a wishbone, but we want this at the angle so that it&#x27;s equivalent to D A. B there. Okay? And using that, um, we start at the point d and make another work, and the ark should overlap left here. If it&#x27;s too short than our angles off, it should overlap. Then we started this next point here, right? Never wear the blue arc intersex with the ray a sea here and just continue the process. And so arcs look something like this. And we know this year I&#x27;ll put it in agree you hear a jumper with the blue arc meets the ray a. C. I&#x27;m in green. And, um, the intersecting points of Ray also agreed. You&#x27;re just so it&#x27;s a little of a color contrast. We have two points which would make a play here. We want to build a drawn line between the two green points here. Here. Right on, Sean. John is best I can, and this is a pretty terrible, terribly scale drawing here. But did you do this correctly and accurately? Um, these will be five equal partitions here originally, it doesn&#x27;t look like that. But with good measurements and practice, these would be five equal partitions there. Well, these air find Michael partitions there. Right? Let&#x27;s say they&#x27;re all equivalent to another. Then partition. 12345 If I want this one for ratio, I placed my point pee right here. Right. And I&#x27;ll divide my segment, baby, into this fight. This, um, by these five vehicle petitions. Now, the question is, why does this work here? Well, let&#x27;s say I haven&#x27;t angle D A b and for triangle J B here, the houses angle. Well, the way we designed these lines here is such that we designed these lines such as these all these lines here on parallel to one another. Okay, now that they&#x27;re all parallel to one another here. Yeah, right. Then if I used each triangle proportionality fair, um, then it divides. It&#x27;s on each triangle. Well, there were decides from he&#x27;s trying so I looked at this small trial which just partition one partition, two partners. 123 and all That in such a way that I have five people partitions. So for reference, let&#x27;s say I look att on the triangle. Go swim! Partition one and two. Okay, here. This is where I&#x27;m eight. Would be this where P would be This is where some point I have. It&#x27;s just some point. This is where partition one is partition to us. These two long two parallel. Let me name them. Um, let&#x27;s try e half engine. Just name them. So it&#x27;s Easter reference. So we want to show here and that a p is equal to P E here. Well, they had to stay in common angle here, okay? And we drew the arcs in such a way that these two lines here and a G is equal to G f. Right. Okay, So by the trunk of proportionality serum here it in seasons of parallel toe another than a p repeat, you action equal in GI or G f of NGOs, G effort. And this should equal one right? Therefore, a p is it was p. So these would be to equal partitions here. And they can repeat this process for the rest of the triangles. I was there, right? So using triangles with partitions 1231234 And so forth It right right here, right in my repeated this process. Then, through the use of the trunk of personality therm, all partitions are calling to one another. So I can definitely place my point p here between at this point here so that we have that one for segment ratio. That&#x27;s why this method works.

Steven Swee · Answer

So this phone or girls trying to draw a two inch line segment and at the point that defines a line segment into a two through issue. So to clarify what this means. If I were to have a line segment Congress line segment A B, um, A and then cook points, it&#x27;s gonna point p that if I take them 92 of Lansing AP and my into the blind segment PB I have this to the three ratio so I can have the length of a P B two and length of PBB three, and I still gets to you through a show. I could have it before and six it 12. As long as I have the suit threw ratio, then, um, I have satisfied the gold. No, just as a little disclaimer. Um, you can easily do this problem, either by just drawing a ruler, having a ruler measuring a two inch line segment and dividing it up into some partitions such that you can have this to three ratio here. So if I have a baby, let&#x27;s pretend this is two inches. Can&#x27;t be. I can&#x27;t find up into five equal parts that I have something to parts here. This is too. The terrible two. Yes, I have suddenly two parts here and something that&#x27;s three parts here. Then I could use this office from easily satisfied to school. And unfortunately, that we&#x27;re looking for used our geometry knowledge to be able to solve Thio complete this problem here with the restriction that can only use the ruler for drawing a 20 minute segment. All right, so we can&#x27;t just divided up by ourselves. Let&#x27;s pretend we don&#x27;t know how to divide up the two inch length. So And also, you could easily follow the instructions in the lesson part of section 8.4 in the textbook. And this bitch is gonna focusing on why, um, the book tells you to construct things. Two inch line segment in the way it does. So it&#x27;s not so. It&#x27;s not gonna be like I&#x27;m gonna tell you each individual step. Rather, what&#x27;s their concepts are there? They&#x27;re behind underlying how the book does its little construction method, so to speak it. So we start off with drawing a two inch line segments here, so I&#x27;m going to pretend I have a pen on start at point a and then draw a two inch line second. Obviously, this is far longer and two inches. You okay? That&#x27;s my two inch line segment. Let&#x27;s pretend switches and I want to build to divide. It&#x27;s not on this length second behind some four point in such a high, this two of the ratio. So the next in the book does is you tells you to write this rape. You seem pretty terrible. The drawing these straight lines. That&#x27;s okay. Quite that&#x27;s decent and ray up to a point c. So when we need to do here here is be able to Johnson Lines, Inc draw some Yes, using arcs ice with a compass. So what we need to do here is we can draw some sort off mark from here, my Justin arbitrary Grady in length arc. And like we said that we can&#x27;t use a ruler, so you can&#x27;t just measure out the compass to be in the up, Link A and B and then divide looking to quarters in your minds, which is he&#x27;s a ruler for that. So one draw. This is Park One, huh? I&#x27;m here and let&#x27;s call this point D and using the same distance were from a to d. Hey, I want to draw another mark, all right? And I keep going. Now, if I wanted to Three ratio here, remember, how has five partition thinking? I&#x27;m gonna create pie partitions, Um, in a B and we don&#x27;t do that here. I do. Um, 123 So this is one partition taken. Partition petition one petition to partition three. I can have partition for and partition fucking me. And also like, your funnel art may not reach point, See, But that&#x27;s okay. So I put that a sz extra points. Yeah, it&#x27;s a point. He and point point g point h injured now, because these are all equal, Like our compass, um, has made these arcs and the distance from one point to another is the same. We can make the statement that a D equals D E vehicles e f equals F g equals G h. And since the entire length is aflame, h and these are five equal parts that I can say that on Lee&#x27;s lengths here or h right, the some entire some of the line segments. And since it&#x27;s 1/5 of the distance, right, so eighties. 1/5 of H. Since it is all equal parts D is 1/5 of age. You sure I can have? It&#x27;s over, and we&#x27;re gonna use the statement later on. And that&#x27;s just not to issue. We have where we un designed these arcs in such a way. It&#x27;s such a beast line segments all equal lengths of h over five. Next thing we need to do here is draw a line, come in HQ to beat. So we get this triangle here, preacher staring into one of brother. Okay. All right. No. The next thing that Brooke wants you to do is measure out this angle. H a b. So over half my little compass, Here&#x27;s a pretty terrible compass. This looks like a wishbone. I have I have this compass here. I want to measure out. This angle here came by which we can do. But I like using a ruler because the compass and measure awesome. Thank you. And I want to make another arc. I started H and make a mark here, and then I started G and make another ark Ark should overlap of its to Shortland. Um then the ankle&#x27;s not correct. in the ark and make another arc. Yeah. Now, what does this do for me? I won&#x27;t. I can&#x27;t put a little put a little thought here is There&#x27;s no point in particular because I&#x27;m mixed on them lying. I&#x27;m here, but I only need two points to make a line. So if I wore to extend this line All right, so take the point. D and they takes intersection right off the two arcs. I could make this line, and I can do the same. And a reason why we do this here, Here. Right. And is that these line segments? Right? Let me call me. Label them with letters first. Uh, let&#x27;s call this I I&#x27;m a j, okay? And he&#x27;s in line Cigarettes here. Our own parallel to one another, including the side. Each bee or triangle h a b there Now, because we have this parallel Tomlinson that seems becoming the triangle. Well, you&#x27;re right. We can use the trying to proportionality there. It&#x27;s a trying proportionality. Thuram, um, to demonstrate why I write our final results here. Right? A eyes with eye J. It was Jake Angles, Kale. He was l b. We&#x27;re just 1/5 of a right, so that&#x27;s kind of alluding to the final answer. So Halloween used trying a portion, at least terrible. Well, let&#x27;s look at the small case there. Harry, um, want me another window? That&#x27;s it. In a small case, he&#x27;s here, and I want to do just recognizing this picture here. Let&#x27;s say I have This is a We put this point h in consciousness point. Well, let&#x27;s say I used a point line segment D right. So let&#x27;s say I have the and this is I here. These are parallel to one another. Here, this green statement appear Idea goes d and supports this Is the statement still valid? So I can say that 80 equals a age for five. First, we&#x27;re just What we&#x27;re doing here is that we&#x27;re just ignoring. Um, the line sings E j f K and G l. For now, I&#x27;m just clean out the picture. So you better see you. What&#x27;s going on? So because license D I h b are parallel to one another, right? India since become the trying on this particular fashion, been by the triangle proportionality thorough, I can say for a reason of apportions that a D over D H is equal to um Aye, aye. Over a be here. Okay. You know well what to be ableto No, nothing. I, um I can observe is that if I might combine a once in a t a n d h Right. So a d plus d h equals h, right? A magnitude I love now since 80 equals age over five and I can substitute age over five plus d h Cols H therefore a D h. Yeah, it was come for a over fuck here. So if I have a job or five, right? So I substitute age over five over for a h five. And if we do the becoming more time by the reciprocal off the denominators that h five times five for H. Well, that gets me one forth just equal to Aye, aye, over a B. So I can sing. This is a length one, and this is of length four and so forth. That&#x27;s why this method works here is because a takes avenge of the trying proportionality. Farum, do you have to divide this bottom line segment into a second ratio? 1 to 4. Now, that&#x27;s our golf gold here. But it is an approach in which, um, do have this partition of wonderful right that&#x27;s given to me to be equal here. So everyone do just fine. Just fine. Which point I jacare l that has this to three ratio. You can probably make an educated guess. So which point passes? 23 vision where I can have a partition here. 1234 500 tropical partitions. I probably want to choose point, Jason. There&#x27;s two petitions from the left and three partitions to my right. So much use to try and proportionality affair. O j proof that point, Jay, is the point me to on a two inch line segment that in order to divide this line segment two to the three ratio So we know that 80 equals deep D e you&#x27;re here. Um, all another slide, I hear. Just make it a little cleaner and then in the previous statements still apply right here. You&#x27;re right. So we have a okay. And B um, we have deny Jimmy, do you? Yeah, I j right. So a d d e a was aged over five. So applies. So Brian Greene, So a d equals D equals a h over five. Now, you can also say bye. Inspection, um, 80 was d e equals a e. Now we do a d plus T. That&#x27;s age of refined plus age over five. This is That means that we have length to H over five. Here. Now, I didn&#x27;t buy the triangle portion. Only thing, right, Because we have lines from E j kind, the triangle in such a way. That lifestyle you, James, Parallel timelines signal hb you here. Then we can say I didn&#x27;t hear that e over e h equals a J. We were j b. Okay, so we know what length 80 is right. But what about th will buy inspection again? We know that e plus e h is equal to mine age. We know the length of 82 b two h five. Okay, so we got substitution, and then we subtract two age over formal science with a length of e h to beat three a eight over five. Nice of you to commit those institutions. So eight years of age. So that would be to eight H over five over 38 h over five. All right, that&#x27;s equal to two h. We&#x27;re five times hive for 388 which equals to over three with that because we have eight year e h bring me that substitution. And because of that 80 over 8 80 over E Ages with a G over J B. So to over three goes a J over J B. So I&#x27;ll be sum this up. Well, we make this line segment Abie to be a link two inches and my phone this method here. But we can say that point, Jay, you ever wherever that point is maybe on your way to finish line segment. I think it&#x27;s 0.0.8 inches away from any and 1.2 inches away from B the race. You want to use the rule to check. Thank you. My devices segment into a to the three ratio here, Since we since we concluded that a J over J B is to over three, I think so. If you want to verify you consider A J here is going to be 0.8 inches and J B is gonna reveal my two inches using a ruler right, and you do this as accurately as you can with compass on this method isn&#x27;t and it is very searching human error, especially a compass a little bit too long or liberty short. Then, um, May gets a number center fairly close, like maybe like 0.9 inches over 1.1 inches. But this is how you would draw a two inch line segment, right, using the ruler on Lee for the case in which you have to draw a line segments to adjust long here and then later on, using a compass. To be able to draw these arcs to divide this line segment into equal partitions, and you choose which point, UM provides a line segment into a 2 to 3 ratio.

James Kiss · Answer

way. Want to find the distance in mid point between the points A, B and B A. Find the distance would be the square roof of the difference of your wife. Ordinate or export its, um a minus B squared. Plus the difference of your, uh why corn? It&#x27;s a B square. The what? It&#x27;s not gonna matter because we spare. It&#x27;s gonna be positive. So we get a swear minus to a B plus B squared, plus a square minus two a B plus B squared. So we get to a square minus for a B plus two he square or the square root of two times a my SP squared, which is the absolutely outing of a minus bi. I&#x27;m suspect root of two because we&#x27;re square rooting this eight square or the midpoint. You just add your exports together a plus B. Take, uh, and you add your wife or in its people is a or a plus and take half

Katelyn Chen · Answer

for this question. We&#x27;re getting a 0.34 and they used the night before and we asked the number things. So for part A were asked a graph this in accordance grid. So we have sorry for over here, and they go through the night before. And this is based on her extrano y cornets. With our first child being exported in our second Ali B Y coordinate party were safe under distances between two points in your distance. You could just square it. Nice reminds three squared last night to formalize Force Word, which will get us 36 plus 64 square. That it&#x27;s within 36 for 64 is equal to 100 so we have the square root of 100 which will get us 10. Next, they asked wonderment. Point the winner would point is equal to three minus 3/2, and then we have met before. That&#x27;s right. Should be just 34 So we have hey before plus four who were too. So that will get us in the end point 00 So these are answers

Problem

a. Draw an acute triangle. Construct the perpendi…

Problem 13 Hard Difficulty

Draw a segment $\overline{A B}$ . Construct a segment $\overline{X Y}$ whose length equals $\frac{3}{4} A B$ .

Answer

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