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Step-by-step explanation: To find the coordinates of V′ in the image of ΔTUV under the given transformations, we can follow these steps:
1. Start with the original coordinates of triangle TUV: T(-1, -1), U(-1, 2), and V(2, 1).
2. Apply the dilation centered at the origin with a scale factor of 5. This means each coordinate of the original triangle will be multiplied by 5.
- For T(-1, -1), the coordinates become T'(-5, -5).
- For U(-1, 2), the coordinates become U'(-5, 10).
- For V(2, 1), the coordinates become V'(10, 5).
3. Next, apply the translation 3 units right and 2 units down. This means we add 3 to the x-coordinate and subtract 2 from the y-coordinate.
- For T'(-5, -5), the coordinates become T''(-2, -7).
- For U'(-5, 10), the coordinates become U''(-2, 8).
- For V'(10, 5), the coordinates become V''(13, 3).
Therefore, the coordinates of V' in the image of ΔTUV under a dilation centered at the origin with a scale factor of 5 followed by a translation 3 units right and 2 units down are V''(13, 3).
