Final answer:
The length of the line segment with endpoints A (-1,9) and B (7,4) is calculated using the distance formula, resulting in approximately 9.4 units. This does not match any of the provided multiple choice options, suggesting a possible typo or error in the question.
Step-by-step explanation:
The question at hand involves determining the length of the line segment with endpoints at A (-1,9) and B (7,4). To do this, we can apply the distance formula which is derived from the Pythagorean theorem:
d = √((x2 - x1)² + (y2 - y1)²)
Where 'd' represents the distance between the two points, (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, x1 = -1, y1 = 9, x2 = 7, and y2 = 4. Plugging in these values we get:
d = √((7 - (-1))² + (4 - 9)²)
d = √((8)² + (-5)²)
d = √(64 + 25)
d = √(89)
The square root of 89 is approximately 9.434, so the length of the line segment is about 9.4 units, which is not one of the provided options. Therefore, the question seems to have a typo or is otherwise incorrect, as none of the options a, b, c, or d match the calculated length.