To determine the quadrant of the point [tex]\((-2, -1)\)[/tex], we need to analyze the coordinates and their signs.
Coordinate system quadrants are defined as follows:
- Quadrant I: [tex]\(x > 0\)[/tex] and [tex]\(y > 0\)[/tex]
- Quadrant II: [tex]\(x < 0\)[/tex] and [tex]\(y > 0\)[/tex]
- Quadrant III: [tex]\(x < 0\)[/tex] and [tex]\(y < 0\)[/tex]
- Quadrant IV: [tex]\(x > 0\)[/tex] and [tex]\(y < 0\)[/tex]
Given the point [tex]\((-2, -1)\)[/tex]:
- The [tex]\(x\)[/tex]-coordinate is [tex]\(-2\)[/tex], which is less than 0.
- The [tex]\(y\)[/tex]-coordinate is [tex]\(-1\)[/tex], which is also less than 0.
Both the [tex]\(x\)[/tex]-coordinate and the [tex]\(y\)[/tex]-coordinate are negative. According to the definitions of the quadrants, a point where both coordinates are negative falls into Quadrant III.
Therefore, the point [tex]\((-2, -1)\)[/tex] is located in Quadrant III.
