Final answer:
The distance between the points (0,-7) and (-9,5) is found using the distance formula. By plugging the coordinates into the formula and simplifying, we find that the distance is 15 units.
Step-by-step explanation:
To find the distance between two points in the Cartesian coordinate system, you can use the distance formula, which is based on the Pythagorean theorem. The formula is:
D = √((x₂-x₁)² + (y₂-y₁)²), where D represents the distance, (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
For the points given, (0,-7) and (-9,5), we plug these values into the formula:
D = √((-9-0)² + (5-(-7))²) = √((-²9)² + (5+7)²) = √(81 + 144) = √225.
The simplest radical form of √225 is 15, because 225 is a perfect square and its positive square root is 15. Therefore, the distance between the two points is 15 units.