What is the angle of rotation about the​ origin, (0,0), that maps triangle PQR to triangle Upper P prime Upper Q prime Upper R prime​?

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Upper PUpper QUpper RUpper P primeUpper Q primeUpper R primeUpper O

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Part 1
Choose the correct answer below.
A.
270degrees
B.
360degrees
C.180 degrees
180degrees
D.90 degrees
90degrees

Answer 1

To determine the angle of rotation that maps triangle PQR to triangle P'Q'R', we first need to analyze the relationships between the points in both triangles.

1. 90 Degrees: Rotating a point 90 degrees counterclockwise around the origin (0,0) puts the point in the specific quadrant to the left of its original position. For example, if a point (x, y) is rotated 90 degrees, it moves to (-y, x).

2. 180 Degrees: Rotating a point 180 degrees around the origin will put the point directly opposite in the coordinate system. For instance, a point (x, y) rotated 180 degrees becomes (-x, -y).

3. 270 Degrees: This is equivalent to a 90-degree clockwise rotation. It moves points in a manner similar but opposite to the 90-degree counterclockwise rotation.

4. 360 Degrees: This is a full rotation that brings the point back to its original location.

To find the correct angle of rotation, you would look for the points of triangles PQR and P'Q'R' to determine the corresponding positions.

Given that the choices only include certain degrees of rotation, if you can observe that the triangles maintain their orientation (i.e., the order of vertices doesn’t change), but are positioned differently, then it would either indicate a 90, 180, or 270-degree rotation.

Without the specific coordinates or a visual representation of the triangles PQR and P'Q'R', we cannot determine the angle definitively. However, if, for example, the triangles can be seen as being flipped across the origin, then the answer would be:

• 180 degrees for a reflection.
• 90 degrees for a quarter turn.
• 270 degrees for three-quarters turn.

Based on the options, if the triangles are in a direct opposite (or rotated completely), C. 180 degrees is the most common response.

If you have specific points or further description of the transformations, I could give a more definitive answer. Based on the options provided previously and common transformations, 180 degrees sounds like the likely expected answer considering a direct opposition would often be the case for triangles being mapped like this.

So, the best answer based on common geometric transformations would likely be:

C. 180 degrees.