Answer:
Explanation:
AI-generated answer
To rotate a triangle 360° clockwise using the origin as the center of rotation, we need to apply the following steps:
1. Find the coordinates of the new vertices of the triangle after rotation.
- To rotate a point (x, y) 360° clockwise around the origin, we can use the formula:
- New x-coordinate = x cosθ - y sinθ
- New y-coordinate = x sinθ + y cosθ
- Since we are rotating the entire triangle, we need to apply this formula to each vertex of the triangle.
2. Apply the rotation formula to each vertex of triangle RST.
- Vertex R(–4, 4):
- New x-coordinate = -4 cos(360°) - 4 sin(360°) = -4
- New y-coordinate = -4 sin(360°) + 4 cos(360°) = 4
- Therefore, the new coordinates for vertex R are (-4, 4).
- Vertex S(–1, 2):
- New x-coordinate = -1 cos(360°) - 2 sin(360°) = -1
- New y-coordinate = -1 sin(360°) + 2 cos(360°) = 2
- Therefore, the new coordinates for vertex S are (-1, 2).
- Vertex T(–3, 0):
- New x-coordinate = -3 cos(360°) - 0 sin(360°) = -3
- New y-coordinate = -3 sin(360°) + 0 cos(360°) = 0
- Therefore, the new coordinates for vertex T are (-3, 0).
3. The new triangle after rotation has vertices R'(-4, 4), S'(-1, 2), and T'(-3, 0).
By rotating triangle RST 360° clockwise using the origin as the center of rotation, the triangle remains unchanged. The new triangle R'S'T' is congruent to the original triangle RST.