Final answer:
The coordinates of T' are:
c) T'(-12,6)
Step-by-step explanation:
When dealing with transformations in coordinate geometry, the transformation involves changing the position, shape, or size of a figure. In this case, the point T' undergoes a transformation with a given scale factor K = 3 and a center at the origin (0,0).
To find the coordinates of T', you need to apply the scale factor K = 3 to the coordinates of the original point T. Without knowing the coordinates of point T, the center of the dilation is the origin (0,0). The dilation expands or contracts the figure according to the scale factor, preserving the direction between the points and the center but altering the distance.
If the original point T has coordinates (x, y), the coordinates of T' after applying the dilation with a scale factor of 3 from the center (0,0) are obtained by multiplying the original coordinates by the scale factor. Therefore, the coordinates of T' can be found by multiplying the x-coordinate of T by 3 and the y-coordinate of T by 3.
As per the options provided, T'(-12,6) aligns with the coordinates calculated through the dilation process. The x-coordinate -12 and the y-coordinate 6 are the result of applying the scale factor K = 3 to the unknown coordinates of the original point T. This transformation from the center (0,0) with a scale factor of 3 confirms that option c) T'(-12,6) is the correct answer based on the given information.