Final answer:
The distance between points A(-1,-5) and B(-4,6) is found using the distance formula, resulting in a value of approximately 11.4 units. Therefore, the correct answer is c) 11.4.
Step-by-step explanation:
To find the distance between two points A and B in a Cartesian plane, you can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is √((x2 - x1)² + (y2 - y1)²).
For the points A(-1,-5) and B(-4,6), the distance calculation is as follows:
- First, determine the differences in x-coordinates and y-coordinates.
- Δx = x2 - x1 = -4 - (-1) = -3
- Δy = y2 - y1 = 6 - (-5) = 11
- Insert these values into the distance formula.
- Distance = √((-3)² + (11)²) = √(9 + 121) = √(130)
- Therefore, the distance is √(130), which is approximately 11.4 units.
The correct answer to the student's question is c) 11.4.