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Assalamualaikum warahmatullahi wabarakatuh. See you again on our channel, Mathematika Hebat. In this video, we will try to discuss the matter of rotation or rotation, about how to determine the point shadow. But before we continue, don't forget to like, subscribe, comment, and share our videos. Hopefully the video is useful and hopefully can be a lesson for us later.
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Now let's discuss the matter with the example of the question. For this rotation matter, it is divided into two parts. The first part is the rotation that is centered at 0,0. Then there is also a rotation that is centered at a,b. For the rotation that is centered at 0,0, it is divided into two parts.
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The first is called positive rotation or the direction of the rotation is against the direction of the clock. This is the summary of the material. Then there is also negative rotation, the direction of the rotation is clockwise. Well, this is the summary of the material.
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Continue for the second part of rotation, which is centered on A,B. To determine the point of the figure or the x-axis, y-axis, it acts as a formula as follows. For a clearer way to use this formula, let's just discuss the example of the problem. Let's look at the first question.
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Determine the image from point A3.1 if rotated 90 degrees counterclockwise with the center O0.0. Pay attention to the steps in its operation. This is very easy. We open the table again earlier, the direction of rotation is counterclockwise. Well, here it is the table, or another term is positive rotation.
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Earlier in the question, we were given a point A, which is 3.1. We are asked to determine the point's dimension. How is the way? This is very easy. Pay attention. Here it is mentioned that if it is rotated 90 degrees, then pay attention to the 90 degree rotation. If we are given a point E, Y here,
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then the shape of the shadow becomes -y,x Remember again, if the point is , then the shadow becomes . Y here is multiplied by negative, it turns into . Well, the x just changes position, it changes to the back. Just like this point A, the shape of the shadow is A-accent. Pay attention again to the way of writing.
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The back number is the first, but it is multiplied by negative. Notice, the back number is the first multiplied by negative. So if 1 is multiplied by negative, the result is negative 1. The front number here remains, only the position changes to the back. So the shape of the image of our first example is A' in the negative 1.3. Well, this is the answer for the first example.
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Easy, isn't it? Very easy and very easy, of course. Well, to understand better, pay attention to the second example. Determine the shadow from point B , if rotated 270 degrees clockwise with the center of O . Okay, pay attention to the steps of the solution.
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Now we open the table again which rotates clockwise. This is the table or another term is called negative rotation. In our question, we are given point B which is negative 2 comma negative 4. We are asked to determine the point.
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Here it is also mentioned that it is rotated 270 degrees. So pay attention to this table, rotate 270 degrees. If we are given the point x, y, then the shape of the image is -y, x. Pay attention to the writing method, x, y.
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Then the image becomes -Y,Y here, which is behind, multiplied by negative, then it becomes -Y. Then this X just moves the position, moves to the back. Then this point B image, or the name of the B-axis, notice negative 4 first, but it is multiplied by negative, then it becomes positive 4. Well,
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The next step, this front number, it just moves the position, moves to the back. This is the second amen. Well, this is the answer form of the second question. It's very easy, of course. Just change the position. God willing, if you already understand these tables, you can easily answer the question about rotation. The key is in this table. Master this table, God willing, you will master the rotation material.
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Moving on to the third question. Determine the image of point C if rotated 90 degrees with the center of rotation at P . Well, this is the rotation of the center of A, B. Okay? How is the solution? This is also very easy. Remember, if there is a point and the center of A, B, then there is a formula to determine the point of the image.
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which is x-axn, y-axn, equal to for x-axn, it is derived from x-a times cos alpha minus y-b times sin alpha plus a then for the value of y-axn, it is derived from x-a times sin alpha plus y-b times cos alpha plus b remember again, x, y here is a dot
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and A, B here, which is the center. If we look at our question this time, the value of X is 3, Y is -5. Then the value of A is 1 and B is 2.
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Now we just have to enter our formula. Change the value of x, y, a, b with what we know in this question. Okay, pay attention. For x - a first. x = 3, a = 1. So here we write 3 - 1. Then multiplied by cos alpha. Alpha here is the value of 90 degrees. So we write here cos 90 degrees. Then subtracted.
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Y - B -5 - 2 Then multiplied by sin alpha Remember alpha here is 90 degrees So here we write sin 90 degrees Then added A, the value of A is 1
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The bottom one again for y-accent, x-a = 3-1, then here the formula is sin alpha, that means sin 90 degrees plus y-b = y-2, then cos alpha, means cos 90 degrees plus b, b here is the value of 2, equal to
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3 - 1 = 2, then cos = 0, then subtracted. -5 - 2 = -7, sin = 1, then finally added 1. The one below again, 3 - 1 = 2.
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multiplied by sin 90, the result is 1. Then add -5 - 2, the result is -7. Then multiplied by cos 90, the result is 0. Finally, add 2, equal to
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2 times 0, the result is 0. Then subtract, negative 7 times 1, the result is negative 7, plus 1. The one below, 2 times 1, the result is 2, then add, negative 7 times 0, the result is 0, then add 2.
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= 0 - -7 + 1 + 8 = 4 So we can calculate the image from this point C
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3.5, the figure is C accent in the 8.4 curve. Well, this is the steps or ways to determine the point figure in the matter of rotation or rotation. It's very easy. So, this is our short tutorial. Hopefully the video is useful. More or less, we apologize. We close with Assalamualaikum Warahmatullahi Wabarakatuh.
