Analisis Bangun Ruang (Dimensi Tiga) Matematika Wajib Kelas XII Bagian 1 - Jarak Titik ke Titik

Assalamualaikum warahmatullahi wabarakatuh, meet again with me Denny Handayani on the MATLAB channel. In this video we will learn one of the subjects that is learned in the 12th grade of compulsory mathematics, namely

Space-building analysis or dimension analysis 3 I will share this material in several separate videos and in this first video we will learn the distance point to point or the distance between points Make sure you watch the video until it's complete because here I will discuss 5 examples of questions with different shapes and at the end of the video there will be a question of training that you can try

Okay, before we discuss the distance from point to point, first of all you have to be able to differentiate what is a point, what is a line, and what is a field.

Pay attention, there is a cube here, cube ABCDEFGH Pay attention, the one represented by letters, ABCDEFGH, is the one called a dot

The point is zero-dimensional, it doesn't have a size. Is the point always in the corner like this? No. For example, add here, the middle between A and B is point P. Usually, the point is described or written with capital letters. This is called a point. Now the line.

Pay attention here, the gap AB, BC, CD, and so on, you know, this gap is A, E, it represents the line, friends. AB, this is the gap AB, this represents the line. The length of the line is not up to, yes. So, for example, the line AB, the line AB means that you can extend it here, like that. But how if it is limited to how long is AB? Well, if you have a long line,

The length is called the line space or segment. Okay? So the length AB, this means the segment, the part of the line. So it is limited from A to B. But if it is only said as a line, the length of the line is not even. So it can be extended here. This can be extended here. Okay? Now these joints are the segment or line space. BC is the same. CG is the same. That's what we call a line. Now the field.

If the field is in dimension 2, it has a long and wide range. For example, here, which one is included? ABCD, this is the base field. This is the field, friends. Then, in front of this, ABFE, this is also a field.

Then the one on the right, BCGF, this is the field. Okay? Now, how many fields does this cube have? It has 6, right? Front, back, left, right, top, bottom. That's what we call the field. Okay, it can be different, right? Now, we will try to discuss some questions.

find the distance from point to point for example from this cube we will find how far is the distance from A to C for example if the length of the curve is known or for example we will find how far is the distance from A to point in the middle of GH if the length of the curve is known okay let's go straight to the example and the explanation

Okay, now we discuss the first question. Known the cube ABCDEFGH with a length of a centimeter. Determine the first one, the distance from point C to F. The second one, the distance from point E to point C. And the third one, the distance from point G to point middle AB. Okay, let's discuss the first one first. The distance from point C to point F. Okay, it means from C to F, this one. Well, we will find the length, friends.

CF is the diagonal of the field or the diagonal of the side. The diagonal of the field or the diagonal of the side. Later the length will be the same as the diagonal of the other side. Where is the diagonal of the side on this cube? Here. EB is also the diagonal of the side. The diagonal of the field. Later the length will be the same as CF.

AF is the same, then from H to C, HC, from G to D, then from E to G, this is the same, all diagonal fields or diagonal sides. From here, from G to B, this is also the same. All diagonal fields or diagonal sides are the same length.

So if we look for CF, it means we have got the length of the other diagonal field. Now we will look for the length of CF. Pay attention to the length of BC and BF, this is a gap, the gap is the length of A, we just write it. The length of BF is A, the length of BC is also A. Now we look at the triangle BCF, this is a triangle on B. We will answer the question A first.

we draw BCF, the sides are on B, the sides are on B, this is B, the sides are here, then C and F, so this is the point C, here is the point F. What we will use is the Pythagorean Theorem, which has been learned during high school. The length of CF, we will find the distance from C to F or the length of CF is the same as

The root of BC squared BC is A, BF is also A BC squared plus BF squared Same as the root of BC, BC is A So A squared plus BF is also A, and A squared Same as the root of A squared plus A squared How much? 2A squared

This is the same as root 2 times root a squared. What is the root of a squared? a squared is rooted, we just remove the squared. So root a squared is a root 2, it remains root 2.

So the length of the diagonal field is a2. So if you are asked how long is ed, for example. This is definitely the same a2 because it enters the diagonal field. If the slope is not a, if the slope is 12. How much is ef? 122. You just have to replace the a. This is also the same. This is also 122 if the slope is a.

Suppose now the slope, for example, in the case of a well, the slope is 16, for example. How long is AC? Come on, how long? AC is the diagonal of the field, the diagonal of the field, yes, the slope is root 2, as we just looked for. So if the slope is 16, AC is 16 root 2, you don't have to count again. Okay, easy, right? Okay, let's continue to section B.

Okay, now we answer section B, how far is it from point E to point C? From E to C. Well, here. This is also a diagonal, but the diagonal that passes into the inner cube is called the space diagonal. Here, where is the space diagonal except E, C?

can also be d to f, df is the same, then from h to b is the same, then from g to a is also the same, all of which are space diagonals, we will look for space diagonals, okay, here the slope is still a, this slope is a, this is a, the height is also the same, friends, pay attention to ac, sorry if it doesn't go straight,

Pay attention to AC, AC is a diagonal field, we have already searched in the A section, the diagonal field if the slope is A, how much? Yes, A root 2, means AC without us counting again, this must be A root 2, because AC is a diagonal field. Now pay attention to slope AE, AE is the same as CG, this is a slope.

So the length is definitely A. Now we will use the triangle ACE. Okay. Part B. Pay attention to the triangle ACE. It's a circle in A. A circle in A. Then here C. The length of AC is A root 2. Then above it is E.

The length of A to E is A. Now we will look for EC, we use Pythagoras too. EC is equal to the root, what is it? AC squared plus AE squared, right? AC squared plus AE squared. Equal to the root, what is the AC? A root 2. We square the root 2, plus AE, A squared too.

a squared is equal to the root a squared is a squared root 2 squared 2 means this a squared root 2 is equal to 2a squared understand ya root 2 squared 2 a squared yes a squared plus a squared so how much? 2a squared plus a squared 3a squared root of a squared is a

So, the length of the space diagonal is a root of 3.

For each cube, if the curve is known, the space diagonal, just add the 3-digit root behind the curve. That's the conclusion. For example, if the curve of the curve is 7 cm, how long is HB? HB is the space diagonal. The length of the curve times the 3-digit root. It must be 7 3 cm.

It's clear? How long is D, F? Same. The space diagonal is also the same. It must be the length of the slope times the root of 3. Simple, right? Remember, the diagonal of the field is times the root of 2, the slope times the root of 2. If the space diagonal is the slope times the root of 3. So the answer for B is A, root of 3. Let's continue to part C.

Okay, now we discuss the C part, how far is the point G to point AB? Point G is to point in the middle of AB. Okay, we assume this is the middle point, which means the distance must be the same.

We call this point P, so P to B and P to A are the same distance, because P is in the middle of AB. We will find the distance from point G to point AB. From G to point AB, here, it means PG, we will find PG. Consider it straight. Because AB is the length of A, the curve is A, AB is the length of A, it means P to B is the middle, this is the middle of A.

A to P is also the same, half of it, this is half A too. Now we need BG, long BG.

Okay, how long is BG? BG is a diagonal field, a diagonal field is a root of root 2. Because the root is A, BG is root 2. Okay, now what we will use is the triangle P, B, G. This is the triangle here, friends. So if we draw, this is the C part. The C part, we will use the triangle P, B, G. Triangle B.

This is P, this is B, this is G. Okay, what is Pb? Half A and Bg is A root 2. We will look for PG. The way is the same, we use Pythagoras here. PG is the same as the root of PB squared, PB squared plus Bg squared. Bg squared is the same as

Pb squared, Pb is half a Half a we square plus bg a root 2 squared Same as Half a squared, half squared is one quarter a squared a squared plus a root 2 squared, the root 2 squared is 2 a squared, yes a squared We make it four times, so that it can be multiplied

This is 1/4a^2, so 2 is equal to how many divided by 4? 8 divided by 4, or 8/4a^2. Understand? We change the 2 to 8/4, so that both are called 4, so we can multiply this. Same as the root of 1/4a^2 + 8/4a^2. 1/4 + 8/4, yes, 9/4.

A squared is equal to 9/4, the root of 9 is 3, the root of 4 is 2, the root of A squared is A. So the answer is 3/2A. So this distance from G to P is 3/2A. What is the unit? Centimeter.

Okay, it's clear, so here Pythagoras is very important If you guys forget, please study the Pythagoras problem again Let's move on to the second question Okay, now we discuss question number 2 Known as the cube ABCDEFGH with a length of 4 cm If the cut of the angle AC and BD is P The distance from point E to point P is Okay, first of all, let's make a picture of the cube ABCDEFGH

This is the image of the cube, A, B, C, D, F, G, pay attention to the name The name is usually opposite the direction of the clock hand, A, B, C, D, then E above A, E, F, G, H, this is the name We will look for, oh yes, how long is the curve? 4 cm

this is 4, this is 4, all 4, 4 cm if the intersection of the joint AC and BD, AC and BD, this is AC and this is BD, means the middle, friends, this is the middle, is the point P, this is the point P, the distance from point E to point P, we will find the distance from E to P, now here, we will find EP, how much is this, okay

Without me counting again, AC is a diagonal field, right? The diagonal field is the same as the root of root 2. So the length of AC is 4 root 2 because the root is 4. AC must be 4 root 2.

Point P is the middle point of AC So AP, PC, then DP, PB, this length is the same Half of the diagonal field So AP is half of 4 root 2, how much? 2 root 2 Then PC is also the same, this is 2 root 2 So P is definitely in the middle Now AE, how long is this? AE is short

which is 4 now we will use the triangle of APE, the triangle is A okay, the triangle of APE, now the AE is 4 then the AP is half of the diagonal of the field which is 2 root 2 we will look for EP, we use Pythagoras too EP is equal to the root of how much? AP squared plus AE squared

AP squared plus AE squared. Same as the root, AP is 2 root 2, 2 root 2 squared plus AE is 4 squared. Same as 2 root 2 squared, root 2 squared is 2, right? 2 squared is 4. So 2 times 4 is 8. This is 8 plus 4 squared is 16.

= 8 + 16 = 24 24 is the same as 4 * 6, right? The root of 4 is 2, the root of 6 is 1 cm So the answer is 2 root 6 cm, the answer is A

Okay, now we discuss question number 3 In the ABCDEFGH cube, the point S is the point located at the length of HD With HD compared to DS equals 2 compared to 1 If the length of the cube is 6 cm, the distance from point F to point S is Okay, let's make the cube first

Okay, the point S is the point located at the length of HD So we lengthen the HD, okay We lengthen it, okay, for example, up to here This is the point S With the ratio of HD to DS is 2: 1 How much is HD? So this is

DS is 1/2 HD HD is a crack, how much is the crack? 6 cm So if the HD is 6, it means this is half of it, friends, 3 because 2 is compared to 1, yes, understand, okay, this is the point S, then we will find the distance from F to S, where is the F, this is the distance from F to S, this is

We will look for the distance f to s We need the length of hf hf is the diagonal of the field Diagonal of the field is the slope times root 2 Remember, the slope times root 2 because the slope was 6, so hf must be 6 root 2 This is the angle of h Now we make the picture more or less like this We take the triangle s, f, h

Imagine, the triangle is S, F, and H. This is a triangle on H, and the other is here. What is the length of Hs? The length of Hs is 6 plus 3. What does it mean? 9. Then the length of Hf is 6, root of 2. We will look for Fs. Fs is the same as, using Pythagoras again, the root of Hf squared plus Hs squared.

HF squared plus HS squared is equal to HF 6 root 2 6 root 2 squared plus HS 9 we square it is equal to

6 square root 2 is squared, 6 squared is 36, square root 2 is 2, 36 times 2 is 72, plus 9 squared is 81. Same as the root of 72 plus 81, 153.

153, okay, pay attention here the choice has all the roots of 17 so it's sure 153 we can divide by 17 this is the same as, okay, it's not enough, I'll continue to this 11, the same as 153 divided by 17 is 9 so it's the same as 9 times 17

What is the 9th root? The 9th root is 3. So this is the same as 3 root 17 centimeters. So the answer is C. 3 root 17 centimeters.

Okay, now we discuss the fourth question. Given the abcdfgh curve with a length of AB 2 cm, BC 4 cm, and AE 2 cm. The distance of the point F to the diagonal cut of the base ABCD. Here we discuss the curve problem. The previous question we discussed the cube. Now we draw the picture first. Pay attention, this is the curve picture.

here the length of AB is 2 cm, we write it, the length of AB is 2 cm BC is 4 cm and AE is 2 cm, the height is 2 cm so the width is 2 cm, the length is 4 cm, the height is 2 cm the distance of the point F to the diagonal cut ABCD ABCD means the diagonal cut here

The cut is here, friends. We assume or we just write it, what is it? Just P, the point is P. We will find the distance from F to P. Here, from F to P, it's not visible. Or it's the same from E to P, the length will be the same. F to P, the length will be the same as from E to P. We need to lengthen AP first, how much is this?

or PC, how much does this mean we need AC first, let's look for AC first, let's look for AC first, to find AC, pay attention to the triangle ABC, this is the line at B, friends, so AC is the same as the root of AB squared plus yes AB squared plus BC squared

BC squared is equal to the root of AB, which is 2 squared 4 plus BC, 4 BC squared here, so 16 is equal to the root of 4 plus 16 20, the root of 20 is the same as 4 times 5, the root of 4 is 2, the root of 5, so AC is 2 root of 5, now AP

a to p is half of ac yes 2 root 5 divided by 2 yes root 5 so ap is root 5 from a to p is root 5 from p to c is also root 5 yes now we will look for ep ep is the triangle of bpf which is this side yes it will be the same as this shape it is here means this is a triangle in b

Fp means bp squared root of bp squared plus bf squared root of bp squared plus bf squared is equal to root of bp, bp is the same as ap from b to p the length will be equal to from a to p root 5 too means here root 5 squared plus bf

From B to F is the same as the height, here 2, 2 square. Equal to the root of 5 squared is 5 plus the root of 2 squared is 4. Equal to the root of 9, root of 9 is 3. So the answer is D, 3 cm.

Okay, now we discuss the last example, question number 5. We have discussed the question about cubes, about blocks, and now we try to discuss the question about squares. Pay attention to the following image. The height of the square T, A, B, C, D in the image is, we will look for the height, friends. We just call it a point, what is this? P again. We will look for PT, how long PT?

This is 5, so TC is 5, right? So TB from T to B is the same. This is 5, then from T to A is also the same, 5, from T to D is also the same, 5. Then the root of the root is 6, so AB is 6, AD is 6, then DC is also the same, 6. We will look for TP.

To find TP, I will use triangle TP C. The triangle is here. So we have to know the length of the PC first. The length from P to C is the same as from A to P. It means it's the same as half of AC. This is the triangle in B. We will look for AC first.

AC is actually a diagonal field, this is definitely a root of root 2. But we use Pythagoras to make it clear. Guys, pay attention to the base, ABCD is square. ABCD. We will look for AC first. We will look for the part here, guys. So if you look from above, the base is square. What is AB? AB is 6. BC is also 6. This is 6, this is 6. This is here. So AC

It's the same as the root of AB squared plus BC squared. The same as the root of 6 squared 36 plus BC is also 6 squared 36. The same as 36 times 2. The root of 36 is 6, so 6 root 2. Well, the AC is 6 root 2. From A to P is half.

What is the half of 6 root 2? 3 root 2 From P to C, it's the same, 3 root 2 Now, let's pay attention to the triangle TPC Triangle TPC Now pay attention to the triangle TPC, it's a circle on P This is a point C and this is a point T How much is TC? 5 cm Then the PC, 3 root 2

3 root 2, now we will look for the height of the five, the height of the five means TP TP we use Pythagoras, equal to the root of, meaning TC squared, minus, TC squared minus PC squared, equal to, TC is 5 squared 25, minus, 3 root 2 squared, 3 squared is 9, 9 times root 2 squared 2

9 times 2 = 18 = 25 - 18 = 7 So the answer is root 7 cm The answer is E Okay, we have discussed 5 examples of questions that are related to the distance between points or the distance point to point Now to test your knowledge how much you understand this material please try the following question

Okay, if you have found the answer, write it in the comments column. See you in the next video. Assalamualaikum warahmatullahi wabarakatuh.