CONSTRUCTION AND LOCUS LIVE LESSON ...

[00:00:30]exhausted.

[00:00:38][clears throat] [clears throat] All right. Hello everyone.

[00:01:18]All right. Hello everyone.

[00:01:34]All right. Today we are going to talk about construction and uh locus.

[00:01:46]So [clears throat] I'm going to work this one. All right.

[00:01:53]I'm going to work on this question extracted from June 2014.

[00:02:05]What I want to do on this question, I just want to construct a quadilateral so that I can teach you different types of locus.

[00:02:18]Okay. [clears throat] So, I'm going to construct this quadilateral as you can see. [clears throat] So it says, "Use a ruler and a compass only for all constructions and show clearly all construction lines and acts."

[00:02:44]Only a single.

[00:02:48]The word single it means one cropped on one diagram on a single diagram on one diagram you must construct this quadilateral.

[00:03:07]A quadilateral is a shape with how many sides? with four sides.

[00:03:19]So do constructor and after constructing it I'm going to teach you some of the things that I want you to to understand.

[00:03:31]Right.

[00:03:35]WX Y Z in which WX is 5A 3 cm.

[00:03:45]WXY is = 120°.

[00:03:51]XY is = 5 cm.

[00:03:57]Y Z is = 9A 1 cm and W Z is = 8 5 cm.

[00:04:11]So on this type of a question I encourage you to do what you call a sketch first.

[00:04:20]Hello, how are you?

[00:04:25]let me know so that I can just shed more light on that particular area. So in four sides it simply means my sketch that I'm going to draw it must be a sketch with four sides.

[00:04:50]So I'm going to draw a sketch here.

[00:04:55]Right. This is a quadrilateral and it's quadrateral x wxy z. And the longest um the the the where the ankle is which is 120 x exactly.

[00:05:12]It simply means X w XY WX. So I'm going to draw WX just like this.

[00:05:33]So this is going to be my W and this is going to be my X. And what is the length of W X? The length is given here. It's 5, 3. What am I doing? I'm drawing a sketch.

[00:05:56]W X Y which is 120 W X or you're going to draw X Y.

[00:06:18]All right. Hope you're listening.

[00:06:21]Let's go. So after that I saw WX Y it simply means this 120° X20 and to make it W X then Y somewhere 121 It's more like 120.

[00:07:17]Then wait.

[00:07:31]which means it's 12.

[00:07:39]Y is in this line.

[00:07:48]XY is= 5 cm.

[00:07:52]Measure 5 cm.

[00:08:06]This is what? 5 cm wa 5 cm.

[00:08:28]This is a sketch.

[00:08:30]The right thing is this is just a sketch.

[00:08:36]No, no.

[00:08:44]Measure 8 5 just like this.

[00:08:56]8 5 to Z Y to Z. It's 9 1 cm 9 8.

[00:09:56]It's 9.

[00:10:21]Remember 5 cm.

[00:10:55]for the sake we are going again to read the question redo the question but now real construction all right this one let us uh work on the question now what is this one says let me just Use another paper. I will put this one as my example.

[00:11:22]So the draw wine end line wx.

[00:11:40]Don't locate any point either. I'm going to locate this point here. I'm going to use this one.

[00:11:47]But this one I'm going to call it W.

[00:11:50]But construction not drawing from W here. From W here to X it's 5 3 cm. So I'm going to measure 5 3 cm. So I measure 5 3 cm.

[00:12:16]And as you can see like this right another another act like this right. What is the angle?

[00:13:00]We have w x y which is 120°.

[00:13:10]All right. X 12.

[00:13:31]It's as simple as that. So like this.

[00:13:52]Which means it's 12.

[00:13:59]X draw a line just like this. All right. WX Y this line WX it means Y is in this line. But how do I know what distance from X to Y is what? It's given question X Y it's 5 cm. So what it means that I'm going to measure 5 cm on my ruler 5 cm right? This is 5 cm.

[00:15:03]Y is here.

[00:15:07]Right. This is quadal. Something with four sides. A shape with four sides.

[00:15:13]Let's go.

[00:15:15]W letter Asara is Z because we are being asked to draw to construct W XY Z. So the only letter that we are left with is letter Z. But what is the length of W to Z? W where is W? W to Z it's 8 comma 5.

[00:15:38]So I'm going to measure again 8a 5 on my ruler.

[00:15:45]So, right 8 5 is here.

[00:16:18]8 comma 5 just like this. Then from there to Z how many cm are there? I'm going to check again on my question. Uh they are saying from Y to Z we have 9A 1 cm. So, what it means is that I'm going back again to my ruler and I measure 9 1 cm. So, I'm going to do that. Mhm. 9 one here. As you can see 9 1 exactly 9 1 here Z what I'm doing is not drawing It is called construction.

[00:17:29]But this is what construction I'm also going to join YZ.

[00:17:46]Right. This is it. So here we have 8a 5 cm. Here we have 9a 1 cm. Here we have what was this? 5 cm.

[00:17:59]And here 5a 3 cm. Then this angle is what? 120°.

[00:18:11]So after doing this I don't know max construction. So this is construction right from here what we are going to do is locas but you can do locasim theories of locus. So let us do what you call theories of locus. So I'm going to remove this paper. I will come back and complete this question. But let me teach you what he call theories of locus.

[00:18:52]All right. Theory number one. I'm going to tell you how zimsek uh mostly ask its questions and how to interpret it. What is the meaning of that question? So theory number one, they will ask you a question like this.

[00:19:13]Construct the locus of points equidistant from equidistant from A and uh B for example. So I'm going to help you understand how to answer this question.

[00:19:46]Remember a certain shape for example shape like this I'm sure triangle A then B then C like this.

[00:20:22]This is drawing. Right.

[00:20:26]Constructing the locus of points equidistant from A and B. What is the meaning of this? The locus of points equidistant from A and B. It simply means bisect line A B. What is to bisect? To biseect it means to divide.

[00:20:54]Saga. What they are saying is divide line A.

[00:21:02]But how do you go about it?

[00:21:06]How do you go about it?

[00:21:10]Like this.

[00:21:20]It's up to you.

[00:21:43]a long act like this.

[00:21:46]Then after that another then draw up.

[00:22:06]So I'm going to draw a line joining these two points of intersection E. So I'm going to draw a line can locus done.

[00:22:29]First theory that you need to understand. Okay.

[00:22:34]Right. Uh theory number two, construct the locus of points equidist equidist equal distance.

[00:22:51]Equid distance means equal distance.

[00:23:07]sector.

[00:23:11]Why does Afra right? Theory number two.

[00:23:34]Construct.

[00:23:38]Constructs the locus of points [snorts] which are 2 cm from a b.

[00:24:02]Can a locus eard construct the locus of points which are 2 cm from AB?

[00:24:14]The locus of points equidist from A and B. He had 2 cm from G.

[00:24:22]I say for example maybe this triangle triangle A B C right on construct the locus of points which are two centers from AB two lines parallel to AB.

[00:25:07]Right? Two lines parallel to AB. It means constructor two lines that we will never meet with AB.

[00:25:19]Right? that will never meet with what 2 cm.

[00:25:32]Then I measure 2 cm using my compass.

[00:25:36]Then measure 2 cm just like this. 2 cm now. All right.

[00:25:52]It's up to you.

[00:25:55]Measure two cm.

[00:26:01]Sorry.

[00:26:15]All right. Anyway, what draw circle can you measure 42 cm right again because right up a circle upfr Right.

[00:27:10]Another line.

[00:27:18]Just like this.

[00:27:21]Right.

[00:27:26]What do we have? 2 cm. Then A going to this parallel line. What do we have? 2 cm.

[00:27:35]Just like this. Depends. Draw two lines that are parallel to AB, which means two lines that we will never meet.

[00:27:51]They will never meet with AB. They are parallel to what to AV. This is the locus. Done.

[00:27:59]Right.

[00:28:01]You are going to have a question like this which is theorem number three. Now theory number three. So on theory number three you are going to be asked a question like this. constructs the locus of points which are 3 cm from B.

[00:28:50]All right. This locus is not difficult.

[00:28:59]They are saying draw a circle with center B and radius what? 3 cm.

[00:29:22]Construct the locus of points which are 3 cm from B.

[00:29:36]Yes. So can a triangle like this.

[00:29:50]Right. Maybe a here then B then C. Right.

[00:30:03]And this is going to be my center.

[00:30:07]Measure given 3 cm. Measure 3 cm.

[00:30:17]Measure 3 cm like this.

[00:30:36]This is the locus.

[00:30:38]Then broken line.

[00:30:44]This is three cm. Done.

[00:30:50]Just draw a circle with center B and the radius being what? 3 cm.

[00:31:00]Then we have a question.

[00:31:04]the sec.

[00:31:07]How to draw the chin the sec.

[00:31:13]So I think a proper question so that I can work on that one triangle.

[00:31:34]Right. Lay one and the triangle PQR with QR equal to 8 cm.

[00:31:49]P QR is 45° and QR P is 60°.

[00:31:59]this one very fast so that I can teach you how to draw a sec line first right so any point. I'm going to call it Q.

[00:32:32]Then we have 8 cm. Measure 8 cm from the ruler.

[00:32:42]8 cm.

[00:33:02]So [clears throat] 8 cm 8 cm.

[00:33:28]Sorry.

[00:33:34]Then Twitter at another Q.

[00:33:59]So this is point R.

[00:34:05][snorts] So question P angle QR is equal 45°.

[00:34:29][clears throat] Say good 45° constructor angle 90.

[00:35:14]>> [snorts] >> So this now change radius. Yes.

[00:35:29]Another angle 90 then towards the radius. Show act.

[00:36:01]It's 90. It's 90° because 45 to 91 after becting 90 right sector So 452 I'm cut.

[00:36:41][snorts] No, it's another arise sector 9 for Not fine.

[00:37:24]So this is 45°.

[00:37:34]Yes, let's continue.

[00:37:36]Don't forget to read your question.

[00:37:38][clears throat] >> Continuation and Q angle RP is equal to degrees.

[00:37:54]point to Godzilla.

[00:38:04]Mhm.

[00:38:14]You went there.

[00:38:16]Yes.

[00:38:31]Act 12 [clears throat] sites.

[00:39:05]degrees.

[00:39:07]It's 120.

[00:39:19]P5.

[00:39:38]>> I thank you.

[00:39:42]>> Right. So Very wonderful. Then 8 cm.

[00:40:01]8 cm.

[00:40:03]All right.

[00:40:23]B sector any two sides going side bctor any two sides sector PQ or QR3.

[00:41:07]Let's go.

[00:41:12]Opening like [snorts] this.

[00:41:26]Another line.

[00:41:37]All right. No line.

[00:41:51]Act like this.

[00:42:03]sector sector 2 by sector P QR PQ is part of your homework.

[00:42:45]Exactly.

[00:43:07]>> [clears throat] >> Up say boy is that correct.

[00:43:50]I want to teach you something.

[00:44:14]Don't question this one.

[00:44:31]Construct the locus.

[00:44:39]Construct the locus of points.

[00:44:53]Which uh which are five cm from Z.

[00:45:18]Construct the locus of points which are 5 cm from Z.

[00:45:34]Measure 5 cm.

[00:45:37]Measure 5 cm.

[00:45:56]Sharp.

[00:45:59]All right.

[00:46:15]Construct the locus of points equidistant from W X and X Y is construct the locus of points equidistant from WX and X WTect.

[00:47:10]The repeated angle in this case [clears throat] XY repeat X Right.

[00:48:07]This Do you have to do construct the locus of points equidistant from WX and XY sector the repeated angle repeat X 2019 [clears throat] rad.

[00:49:39]Right.

[00:49:52]Right. The reason whatever You must have at least two locals.

[00:50:11][snorts] Shed the region.

[00:50:20]For example, sh the region that is that is less than 5 cm from from Z and near two and nearer to near and nearer to Z and there are two Y Z then W Z less and 5 cm inside the quad. make a sense inside the the region right inside The as less than five sector is man-made question.

[00:52:52]Right.

[00:53:02]Less than right.

[00:53:17]And that region to wx than xy then xy but wx as compared to xy one region less than 5 cm taiwan WX WX WX guide to WXY XY very less than five WX Y less than 5 cm WXY What?

[00:54:51]Horn [clears throat] sector.

[00:55:11]Right.

[00:55:22]Construction of points which are 5 cm from Exactly.

[00:55:44]>> [snorts] >> 5 cm.

[00:55:48]Right.

[00:55:51]Shade the region inside the triangle. And which are [clears throat] less than 5 cm and nearer to nearer to A than B.

[00:56:39]triangle.

[00:56:45]The triangle is less than 5 cm.

[00:56:58]triangle but less than 5 cm a b of I think correct.

[00:58:07]Measure the length of AC.

[00:58:18]>> [laughter] >> 6 9 6 9 cm. Done.

[00:58:43]Size of the angle. A B C.

[00:58:55]work.

[00:58:59][laughter] [laughter] Hey.

[00:59:08]Hey.

[00:59:17]All right.

[00:59:41]up.

[00:59:44][clears throat] Right. Second reading. It's 0 10 20 30 40 50 1 there a B C it's what [snorts] it's it's it's one there one it's better.

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