Final Answer:
The distance between the points (4, -2) and (9, -5) is 5 units.
Explanation:
To find the distance between the two points, we can use the distance formula, which is given by √((x2-x1)² + (y2-y1)²). Substituting the given coordinates, we get √((9-4)² + (-5-(-2))²), which simplifies to √(5² + (-3)²), and further simplifies to √(25 + 9), resulting in √34. Therefore, the distance between the points is √34 units, which is approximately 5 units when rounded to the nearest whole number.
The distance formula is derived from the Pythagorean theorem, where the distance between two points in a coordinate plane is represented by the hypotenuse of a right-angled triangle. By applying this formula to the given points, we can calculate the length of the line segment connecting them. In this case, the horizontal distance between the points is 5 units (9-4), and the vertical distance is 3 units (-5-(-2)). Using these values in the formula yields the final result of approximately 5 units for the distance between the points.
In summary, by using the distance formula and substituting the given coordinates into it, we found that the distance between the points (4, -2) and (9, -5) is approximately 5 units. This method provides a straightforward way to calculate distances between any two points in a coordinate plane.