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Answer:
30° rotation and another 330° rotation about the same point is equivalent to 30+330 = 3600° rotation about that point
Which brings it back to the initial position
The image of ∆XYZ for a composition of a 30° rotation and a 330° rotation, both about point Z will be the triangle itself. The correct option is B, Image 3.
What is a triangle?
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
A complete rotation forms an angle of 360°, about the point through which it is rotated.
Since it is given that the ∆XYZ has a rotation of 30° and 330°, about the point Z. Therefore, the total rotation of the triangle about the point Z is,
Total rotation = 30° + 330°
= 360°
Further, since the total rotation is 360°. Therefore, the triangle will be the same after the complete rotation.
Hence, the image of ∆XYZ for a composition of a 30° rotation and a 330° rotation, both about point Z will be the triangle itself. The correct image is the third image.
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