To determine the coordinate of [tex]\( B' \)[/tex] under a scale factor of 3, we need to understand how scaling affects the coordinates of a point.
Given the coordinates of point [tex]\( B \)[/tex] as [tex]\( B(1,-1) \)[/tex], let's apply the scale factor:
1. Identify the original coordinates:
The coordinates of point [tex]\( B \)[/tex] are [tex]\( (1, -1) \)[/tex].
2. Apply the scale factor to each coordinate:
- For the x-coordinate: Multiply the x-coordinate by the scale factor: [tex]\( 1 \times 3 = 3 \)[/tex].
- For the y-coordinate: Multiply the y-coordinate by the scale factor: [tex]\( -1 \times 3 = -3 \)[/tex].
3. Determine the new coordinates:
The new coordinates of point [tex]\( B' \)[/tex] are [tex]\( (3, -3) \)[/tex].
So, the coordinate of [tex]\( B' \)[/tex] under a scale factor of 3 is [tex]\( (3, -3) \)[/tex].
Therefore, the correct answer is [tex]\( (3, -3) \)[/tex].
