Let's determine the quadrant of the point [tex]\((-3, -14)\)[/tex] in the [tex]\((x, y)\)[/tex]-coordinate plane.
1. Identifying the signs of the coordinates:
- The [tex]\(x\)[/tex]-coordinate is [tex]\(-3\)[/tex], which is less than 0.
- The [tex]\(y\)[/tex]-coordinate is [tex]\(-14\)[/tex], which is also less than 0.
2. Understanding the quadrants:
- Quadrant I: Both [tex]\(x\)[/tex] and [tex]\(y\)[/tex] coordinates are positive.
- Quadrant II: [tex]\(x\)[/tex] is negative, and [tex]\(y\)[/tex] is positive.
- Quadrant III: Both [tex]\(x\)[/tex] and [tex]\(y\)[/tex] coordinates are negative.
- Quadrant IV: [tex]\(x\)[/tex] is positive, and [tex]\(y\)[/tex] is negative.
3. Analyzing the coordinates of the point [tex]\((-3, -14)\)[/tex]:
- Since both the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] coordinates of the point [tex]\((-3, -14)\)[/tex] are negative, we can conclude the point lies in Quadrant III.
Therefore, the point [tex]\((-3, -14)\)[/tex] is in:
C) Quadrant III
