Question

In order to receive full credit, you must explain your answer.
The coordinates (-9,2). (-12,5), and (-5,7) were plotted on a coordinate plane, and a polygon was drawn. Is the polygon in Quadrant I, II, III, or IV?
• Quadrant I
• Quadrant II
•.
Quadrant III
• Quadrant IV

Answer 1

To determine which quadrant the polygon formed by the points (-9, 2), (-12, 5), and (-5, 7) resides in, we first need to identify the positioning of each of these points in relation to the quadrants on a coordinate plane.

In a standard Cartesian coordinate system:

- **Quadrant I** is where both x and y values are positive (x > 0, y > 0).
- **Quadrant II** is where x is negative and y is positive (x < 0, y > 0).
- **Quadrant III** is where both x and y values are negative (x < 0, y < 0).
- **Quadrant IV** is where x is positive and y is negative (x > 0, y < 0).

Now, we analyze the given coordinates:

1. **Point (-9, 2)**: Here, x is -9 (negative) and y is 2 (positive). Hence, this point lies in **Quadrant II**.
2. **Point (-12, 5)**: Here, x is -12 (negative) and y is 5 (positive). Hence, this point also lies in **Quadrant II**.
3. **Point (-5, 7)**: Here, x is -5 (negative) and y is 7 (positive). Hence, this point too lies in **Quadrant II**.

Since all three points lie in Quadrant II, the polygon formed by connecting these points will also lie in Quadrant II.

Thus, the final answer is:
**Quadrant II**.