To determine where the point [tex]\((-10, 0)\)[/tex] is located, we need to consider its coordinates and understand the structure of the coordinate system:
1. The coordinate system is divided into four quadrants by the [tex]\(x\)[/tex]-axis and the [tex]\(y\)[/tex]-axis:
- Quadrant I: Both [tex]\(x\)[/tex] and [tex]\(y\)[/tex] coordinates are positive.
- Quadrant II: [tex]\(x\)[/tex] coordinate is negative, [tex]\(y\)[/tex] coordinate is positive.
- Quadrant III: Both [tex]\(x\)[/tex] and [tex]\(y\)[/tex] coordinates are negative.
- Quadrant IV: [tex]\(x\)[/tex] coordinate is positive, [tex]\(y\)[/tex] coordinate is negative.
2. The axes themselves are special cases:
- Points along the [tex]\(x\)[/tex]-axis have a [tex]\(y\)[/tex] coordinate of 0.
- Points along the [tex]\(y\)[/tex]-axis have an [tex]\(x\)[/tex] coordinate of 0.
Given the point [tex]\((-10, 0)\)[/tex]:
- The [tex]\(x\)[/tex] coordinate is [tex]\(-10\)[/tex], which is negative.
- The [tex]\(y\)[/tex] coordinate is [tex]\(0\)[/tex].
Since the [tex]\(y\)[/tex] coordinate is [tex]\(0\)[/tex] and the [tex]\(x\)[/tex] coordinate is nonzero, the point lies exactly on the [tex]\(x\)[/tex]-axis.
Therefore, the correct answer is:
C) [tex]\(x\)[/tex]-axis
