Final answer:
The distance d(A,B) between points A(2,9) and B(-5,-2) is calculated using the distance formula, resulting in approximately 13.04 units.
Step-by-step explanation:
To find the distance d(A,B) between points A(2,9) and B(-5,-2), we use the distance formula derived from the Pythagorean theorem, which is:
d(A,B) = √((x2 - x1)² + (y2 - y1)²)
We denote A as (x1,y1) and B as (x2,y2). By plugging in the values from point A(2,9) for (x1,y1) and point B(-5,-2) for (x2,y2), we get:
d(A,B) = √((-5 - 2)² + (-2 - 9)²) = √((-7)² + (-11)²) = √(49 + 121) = √(170)
Therefore, the distance between points A and B is the square root of 170, which is approximately 13.04 units.