Final answer:
The pairs located in the third quadrant are (-3,-1) and (-4,-6), as points in the third quadrant are characterized by both x and y coordinates being negative.
Step-by-step explanation:
The question is asking to identify which points are located in the third quadrant of the coordinate grid. In the coordinate system, points in the third quadrant have both x and y coordinates as negative values, because the third quadrant is located horizontally to the left side of the coordinate system and vertically downward in the coordinate system.
Now, let's examine the given options:
- (2,-8): This pair has a positive x value and a negative y value, which places it in the fourth quadrant, not the third.
- (-3,-1): Both x and y values are negative, so this pair is indeed in the third quadrant.
- (5,4): Both x and y values are positive, placing this point in the first quadrant.
- (-4,-6): Like the second point, this one also has negative values for both x and y, which means it is in the third quadrant.
Therefore, the pairs located in the third quadrant are (-3,-1) and (-4,-6).