To determine the coordinates of the vertices of triangle CAT after a 270Β° counterclockwise rotation about the origin, we can use the formula for rotating a point \((x, y)\) by an angle \(\theta\):
- The coordinates after rotation are: \[ (x', y') = (x \cdot \cos(\theta) - y \cdot \sin(\theta), x \cdot \sin(\theta) + y \cdot \cos(\theta)) \]
For a 270Β° counterclockwise rotation, we can convert this angle into radians as follows: \[ 270^\circ = \frac{3\pi}{2} \text{ radians} \] Using trigonometric values:
- \(\cos(270^\circ) = 0\)
- \(\sin(270^\circ) = -1\)
The rotation formulas simplify to: \[ (x', y') = (y, -x) \]
Now, we will apply this transformation to each vertex of triangle CAT. Let's assume the original coordinates are:
- \(C(x_1, y_1)\)
- \(A(x_2, y_2)\)
- \(T(x_3, y_3)\)
After the 270Β° rotation, the transformed coordinates will be:
- \(C'(y_1, -x_1)\)
- \(A'(y_2, -x_2)\)
- \(T'(y_3, -x_3)\)
You need to check if the given coordinates:
- \(C'(1,-1)\)
- \(A'(7,-5)\)
- \(T'(2,-5)\)
correspond to the original triangle vertices after rotation.
Now, without knowing the original vertices' coordinates, we cannot definitively state if the new coordinates are correct. However, if you have the original coordinates before the rotation, please provide them, and I can verify if the rotated coordinates match.
Based solely on the provided options, the response would be "No" unless the original coordinates also support the final given coordinates after rotation.
Response: No