Final answer:
The distance between the points (-6,-7) and (3,-4) is found using the distance formula resulting in 3√10 or approximately 9.49 units.
Step-by-step explanation:
To find the distance between the points (-6,-7) and (3,-4), we use the distance formula which is derived from the Pythagorean theorem. The formula is given by:
Distance = √((x2 - x1)² + (y2 - y1)²)
Here, (x1, y1) = (-6, -7) and (x2, y2) = (3, -4). Substituting these values into the formula gives us:
Distance = √((3 - (-6))² + (-4 - (-7))²)
Distance = √((3 + 6)² + (-4 + 7)²)
Distance = √(9² + 3²)
Distance = √(81 + 9)
Distance = √90
Distance = 3√10 or approximately 9.49 units.
Therefore, the distance between the two points is 3√10, which is approximately 9.49 units.