Final answer:
To find the distance between the points (2,5) and (-3,-3), the distance formula d = √((x_2-x_1)^2 + (y_2-y_1)^2) is applied, resulting in an approximate distance of 9.43 units, which is not listed in the given answer choices.
Step-by-step explanation:
The question asks for the length of the segment between the points (2,5) and (-3,-3). To find this, we can use the distance formula which is derived from the Pythagorean theorem. The formula is d = √((x_2-x_1)^2 + (y_2-y_1)^2), where d represents the distance between two points, (x_1, y_1) and (x_2, y_2) are the coordinates of the two points.
Applying the formula to the points given, we get:
- Identify the coordinates as (x_1, y_1) = (2, 5) and (x_2, y_2) = (-3, -3).
- Substitute the values into the formula: d = √((-3 - 2)^2 + (-3 - 5)^2)
- Simplify the equation: d = √((-5)^2 + (-8)^2) = √(25 + 64)
- Further simplify the equation: d = √(89)
- Calculate the square root: d ≈ 9.43
However, since the options given in the question do not include this value, it seems there may be a mistake in the question or the answer choices. The correct distance is approximately 9.43 units, which is not listed in the available options.