To determine which value could be the [tex]\( y \)[/tex]-coordinate for point [tex]\( Q \)[/tex] with an [tex]\( x \)[/tex]-coordinate of [tex]\( 4 \)[/tex], we need to examine the given options numerically.
1. Option [tex]\( 2 \sqrt{5} \)[/tex]:
[tex]\[
2 \sqrt{5} \approx 2 \times 2.236 = 4.472
\][/tex]
This value approximately equals [tex]\( 4.472 \)[/tex].
2. Option [tex]\( 4 \sqrt{2} \)[/tex]:
[tex]\[
4 \sqrt{2} \approx 4 \times 1.414 = 5.657
\][/tex]
This value approximately equals [tex]\( 5.657 \)[/tex].
3. Option [tex]\( 2 \sqrt{13} \)[/tex]:
[tex]\[
2 \sqrt{13} \approx 2 \times 3.606 = 7.211
\][/tex]
This value approximately equals [tex]\( 7.211 \)[/tex].
4. Option [tex]\( 8 \sqrt{2} \)[/tex]:
[tex]\[
8 \sqrt{2} \approx 8 \times 1.414 = 11.314
\][/tex]
This value approximately equals [tex]\( 11.314 \)[/tex].
Given the potential numeric values, the possible [tex]\( y \)[/tex]-coordinates for point [tex]\( Q \)[/tex] are:
- [tex]\( 4.472 \)[/tex]
- [tex]\( 5.657 \)[/tex]
- [tex]\( 7.211 \)[/tex]
- [tex]\( 11.314 \)[/tex]
Therefore, the potential [tex]\( y \)[/tex]-coordinate for point [tex]\( Q \)[/tex] can be one of these values that match the respective approximations from the given options:
[tex]\[ 4.472, 5.657, 7.211, \text{ and } 11.314 \][/tex]
Hence, any of the following could be a valid [tex]\( y \)[/tex]-coordinate:
- [tex]\( 2 \sqrt{5} \approx 4.472 \)[/tex]
- [tex]\( 4 \sqrt{2} \approx 5.657 \)[/tex]
- [tex]\( 2 \sqrt{13} \approx 7.211 \)[/tex]
- [tex]\( 8 \sqrt{2} \approx 11.314 \)[/tex]
These calculations confirm that the [tex]\( y \)[/tex]-coordinate for point [tex]\( Q \)[/tex] can indeed be one of these values provided in the question.
