To solve this problem, we need to identify the original coordinates of point [tex]\( Q \)[/tex] given the transformed coordinates [tex]\( Q^{\prime} \)[/tex]. We start with the information that we have:
- The transformed coordinates of the vertices of the rectangle are [tex]\( R^{\prime}(-4,4) \)[/tex], [tex]\( S^{\prime}(-4,1) \)[/tex], [tex]\( P^{\prime}(-3,1) \)[/tex], and [tex]\( Q^{\prime}(-3,4) \)[/tex].
These points form the image of the rectangle after transformation.
Given that the transformation rule is not changing the coordinates in this particular case, we conclude that the original position of [tex]\( Q \)[/tex] is the same as its final position. This is illustrated by:
1. We observe the location of [tex]\( Q^{\prime} \)[/tex], which is [tex]\( (-3, 4) \)[/tex].
Thus, the coordinates of [tex]\( Q \)[/tex] are:
[tex]\[ (-3, 4) \][/tex]
Comparing these coordinates with the given options, we see that the correct option is:
[tex]\[
(-3, 4)
\][/tex]
