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Point [tex]\( B \)[/tex] has coordinate [tex]\( B(1, -1) \)[/tex]. What is the coordinate of [tex]\( B^{\prime} \)[/tex] under a scale factor of 3?

A. [tex]\( (1, -1) \)[/tex]
B. [tex]\( (3, -3) \)[/tex]
C. [tex]\( (-2, 2) \)[/tex]
D. [tex]\( (-6, 6) \)[/tex]

Sagot :

GinnyAnswer
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].
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