To determine which point has the coordinates [tex]\(\left(5, -\frac{7\pi}{6}\right)\)[/tex], we need to examine the coordinates given for each point.
Here are the coordinates for each point:
- Point [tex]\( A \)[/tex]: [tex]\(\left(5, -\frac{7\pi}{6}\right)\)[/tex]
- Point [tex]\( B \)[/tex]: [tex]\(\left(5, -\frac{2\pi}{6}\right)\)[/tex]
- Point [tex]\( C \)[/tex]: [tex]\(\left(5, -\frac{3\pi}{6}\right)\)[/tex]
- Point [tex]\( D \)[/tex]: [tex]\(\left(5, -\frac{\pi}{2}\right)\)[/tex]
Comparing each point's coordinates with the given coordinates [tex]\(\left(5, -\frac{7\pi}{6}\right)\)[/tex]:
- Point [tex]\( A \)[/tex] has coordinates [tex]\(\left(5, -\frac{7\pi}{6}\right)\)[/tex].
- Point [tex]\( B \)[/tex] has coordinates [tex]\(\left(5, -\frac{2\pi}{6}\right)\)[/tex]. This does not match.
- Point [tex]\( C \)[/tex] has coordinates [tex]\(\left(5, -\frac{3\pi}{6}\right)\)[/tex]. This does not match.
- Point [tex]\( D \)[/tex] has coordinates [tex]\(\left(5, -\frac{\pi}{2}\right)\)[/tex]. This does not match.
Only Point [tex]\( A \)[/tex] has the matching coordinates of [tex]\(\left(5, -\frac{7\pi}{6}\right)\)[/tex].
Therefore, the point with coordinates [tex]\(\left(5, -\frac{7\pi}{6}\right)\)[/tex] is Point [tex]\( A \)[/tex].
