Final answer:
The length of line segment AB with endpoints A = (4, -5) and B = (7, -9) is calculated using the distance formula: d = √((x2 - x1)² + (y2 - y1)²) which equals 5 units. The provided options in the question seem to contain an error as none match the correct calculation.
Step-by-step explanation:
To find the length of segment AB with endpoints A = (4, -5) and B = (7, -9), we use the distance formula which is derived from the Pythagorean theorem. The formula to calculate the distance between two points A(x1, y1) and B(x2, y2) in a coordinate plane is d = √((x2 - x1)² + (y2 - y1)²).
Substituting the given coordinates:
- x1 = 4, y1 = -5
- x2 = 7, y2 = -9
We compute:
d = √((7 - 4)² + (-9 - (-5))²)
d = √((3)² + (-4)²)
d = √(9 + 16)
d = √25
d = 5 units
The correct answer, which is the length of AB, would be option c) √34, but since our calculation gives us 5, there is an error in the provided options or a mistake in the calculations. To clarify, the correct calculation of the length of AB using the provided points is 5 units, and none of the given options matches this answer.