To determine the coordinates of [tex]\( B' \)[/tex] under a scale factor of 3, we start with the original coordinates of point [tex]\( B \)[/tex], which are [tex]\( (1, -1) \)[/tex].
Scaling a point involves multiplying each coordinate of the point by the scale factor. Here, our scale factor is 3. Let's apply this step-by-step:
1. Starting coordinates of point [tex]\( B \)[/tex]:
- [tex]\( x = 1 \)[/tex]
- [tex]\( y = -1 \)[/tex]
2. Apply the scale factor to the [tex]\( x \)[/tex]-coordinate:
[tex]\[
x' = 1 \times 3 = 3
\][/tex]
3. Apply the scale factor to the [tex]\( y \)[/tex]-coordinate:
[tex]\[
y' = -1 \times 3 = -3
\][/tex]
Thus, after scaling, the new coordinates of point [tex]\( B \)[/tex] are:
[tex]\[
(x', y') = (3, -3)
\][/tex]
So, the coordinate of [tex]\( B' \)[/tex] under a scale factor of 3 is [tex]\( \boxed{(3, -3)} \)[/tex].
