Final answer:
The distance between the points (-5,2) and (-8,5) is calculated using the distance formula, resulting in a distance of √(18), or 3√(2).
Step-by-step explanation:
The question asks to find the distance between the two points (-5,2) and (-8,5). To calculate this distance, we use the distance formula, which in two dimensions is the square root of the sum of the squares of the differences in the x-values and y-values respectively. In mathematical terms, the distance d between two points (x1, y1) and (x2, y2) is given by the formula:
d = √((x2 - x1)^2 + (y2 - y1)^2).
By substituting the given values, we have:
d = √((-8 - (-5))^2 + (5 - 2)^2) = √((-3)^2 + (3)^2) = √(9 + 9) = √(18).
Therefore, the distance between the points is √(18), which can also be simplified to 3√(2) if required.