To determine in which quadrant the polygon formed by the points (9,−2), (12,−5), and (5,−7) lies, we can look at the coordinates of the points:
- (9,−2) - This point is in Quadrant IV (x is positive, y is negative).
- (12,−5) - This point is also in Quadrant IV (x is positive, y is negative).
- (5,−7) - This point is again in Quadrant IV (x is positive, y is negative).
Since all three points are in Quadrant IV, the polygon formed by these points is also entirely in Quadrant IV.
The answer is 4 (for Quadrant IV).