Given the problem, we need to determine which set of vertices represents the correct image of the triangle [tex]\(UVW\)[/tex] after a rotation. The original vertices of the triangle are:
[tex]\[ U(-2, 0), \quad V(-3, 1), \quad W(-3, 3) \][/tex]
We are given four options for the vertices of the rotated image [tex]\(U^{\prime} V^{\prime} W^{\prime}\)[/tex]:
1. [tex]\( U^{\prime}(0, -2), \quad V^{\prime}(-1, -3), \quad W^{\prime}(-3, -3) \)[/tex]
2. [tex]\( U^{\prime}(0, -2), \quad V^{\prime}(1, -3), \quad W^{\prime}(3, -3) \)[/tex]
3. [tex]\( U^{\prime}(2, 0), \quad V^{\prime}(3, -1), \quad W^{\prime}(3, -3) \)[/tex]
4. [tex]\( U^{\prime}(-1, 0), \quad V^{\prime}(-3, 0), \quad W^{\prime}(3, -3) \)[/tex]
Now, let’s determine the correct set of vertices [tex]\(U^{\prime}, V^{\prime}, W^{\prime}\)[/tex] that matches the image of the original triangle after rotation. After rotation, the vertices are given as:
[tex]\[ U^{\prime}(0, -2), \quad V^{\prime}(1, -3), \quad W^{\prime}(3, -3) \][/tex]
Therefore, the correct option is:
2. [tex]\( U^{\prime}(0, -2), \quad V^{\prime}(1, -3), \quad W^{\prime}(3, -3) \)[/tex]
