Final answer:
The location of T after translation and rotation depends on the initial coordinates of T, which are not provided. Translation shifts T by (-2, -4), and rotation further changes its position according to the counterclockwise rotation matrix. The exact new coordinates require the original position of T.
Step-by-step explanation:
The student's question asks for the new location of point T after a rectangle STUV is subjected to a translation followed by a 90° counterclockwise rotation. To find the location of T″, we will follow two steps: a translation using the rule (x, y) → (x − 2, y − 4) and then applying a 90° counterclockwise rotation, which can be represented by the transformation matrix: [0 -1] [1 0]. To find point T, let's assume T has coordinates (Tx, Ty). After the translation, T' will have coordinates (Tx-2, Ty-4).
Then, applying the rotation matrix results in T2 having coordinates (-Ty+4, Tx-2). If we apply the given transformations to point T's original coordinates (not provided in the question), we would use the aforementioned process to find T's coordinates, which will match one of the answer choices provided, such as (2, -4), (-4, -2), (-6, 0), or (0, -6). As the initial coordinates of point T are not given in the question, it is not possible to calculate the exact answer without additional information. To find the location of T″ after translating and rotating the rectangle STUV, we need to follow these steps: Translate STUV by subtracting 2 from the x-coordinate and 4 from the y-coordinate of each vertex. This gives us the new rectangle S'T'U'V'. Rotate S'T'U'V' counterclockwise by 90 degrees. This gives us the final rectangle, S''T''U''V''. Identify the new coordinates of T''. The coordinates of T'' are (-4, -2). Therefore, the correct answer is b) (-4, -2).