How To Find The Rotation Center For Triangle Transformations Step By Guide
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Learn how to pinpoint the rotation center when transforming triangle ABC to A'B'C'. Follow a logical step-by-step process and discover the intersection of perpendicular bisectors.
- This video explains how to find the rotation center when mapping triangle ABC to triangle A'B'C' through a transformation.
- The process involves connecting corresponding points, drawing perpendicular bisectors, and checking for equal line segment lengths.
- The rotation center is identified as the intersection of these perpendicular bisectors.
In the video "Transformation How to Find the Rotation Center," the presenter walks us through a comprehensive approach to determine the rotation center when mapping one triangle onto another. This process involves connecting corresponding points, drawing perpendicular bisectors, and verifying the equality of line segment lengths. By the end, you'll gain a clear understanding of how to identify the rotation center for a given transformation.
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Step 1 Estimating Rotation
- Start by assessing whether the figure has been rotated by 180 degrees. By applying logical reasoning, you can deduce if a 180-degree rotation has occurred.
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Step 2 Connecting Corresponding Points
- Once it's determined that the figure hasn't undergone a 180-degree rotation, proceed to connect the corresponding points of the two triangles. In this example, points A and A' are selected for the first pair.
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Drawing Perpendicular Bisectors
- Using a compass, draw the perpendicular bisector of the line connecting points A and A'. This creates a crucial line segment.
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Selecting Appropriate Points
- In selecting points for the second pair, it's essential to avoid parallel lines. In this case, points C and C' are chosen. The intersection of the two perpendicular bisectors is the rotation center, which is labeled as point R.
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Step 3 Checking the Point
- Since the lines are drawn manually, there might be slight errors due to accidental movements. To confirm the accuracy, connect the corresponding points to point R and check if the line segment lengths are equal. In this example, line segments RA and RA', as well as RC and RC', are confirmed to be equal.
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Explaining the Concept
- To understand why this method works, it's helpful to revisit the fundamentals of rotation. When a point, such as A, is rotated, it is equivalent to drawing a circle with point R as the center and the line AR as the radius. Points A and A' are found on the same circle, and the line segment AA' becomes a chord of this circle.
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Perpendicular Chord Bisector Theorem
- According to the perpendicular chord bisector theorem, point R lies on the perpendicular bisector of the line segment AA', as well as on the bisectors of line segments BB' and CC'. The intersection of all these perpendicular bisectors is the center of the set of concentric circles.
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Determining the Rotation Center
- In cases where point A is rotated 180 degrees, point A and A" form the two end points of a diameter of the circle. The middle point of this connection is the rotation center. In the example provided, the rotation center is identified as point R.
By following this systematic approach, you can ascertain the rotation center for any given transformation. This method is particularly useful for understanding how triangle ABC is rotated 90 degrees clockwise around point R to achieve triangle A'B'C'. If you found this explanation helpful, be sure to subscribe to the presenter's channel for more informative content. Thank you for watching!
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