To determine which quadrant the ordered pair [tex]\((-7, -5)\)[/tex] lies in, we examine the signs of the coordinates [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
Let's recall the conditions for each quadrant:
- Quadrant 1: [tex]\(x > 0\)[/tex] and [tex]\(y > 0\)[/tex]
- Quadrant 2: [tex]\(x < 0\)[/tex] and [tex]\(y > 0\)[/tex]
- Quadrant 3: [tex]\(x < 0\)[/tex] and [tex]\(y < 0\)[/tex]
- Quadrant 4: [tex]\(x > 0\)[/tex] and [tex]\(y < 0\)[/tex]
For the point [tex]\((-7, -5)\)[/tex]:
- The [tex]\(x\)[/tex]-coordinate is [tex]\(-7\)[/tex], which is less than 0.
- The [tex]\(y\)[/tex]-coordinate is [tex]\(-5\)[/tex], which is also less than 0.
Both the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] coordinates are negative.
According to the conditions:
- When both [tex]\(x < 0\)[/tex] and [tex]\(y < 0\)[/tex], the point lies in Quadrant 3.
Therefore, the ordered pair [tex]\((-7, -5)\)[/tex] is found in quadrant 3.
