Apply the Distance Formula

To find the length of the line segment with endpoints (4, 7) and (1, 11), we can use the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance = √((1 - 4)^2 + (11 - 7)^2)
Distance = √((-3)^2 + (4)^2)
Distance = √(9 + 16)
Distance = √25
Distance = 5

So, the length of the given line segment is 5.

The line segment with endpoints (1, - 4) and (9, 2) is equal in distance to the given line segment:

To find the distance of this line segment:

Distance = √((9 - 1)^2 + (2 - (-4))^2)
Distance = √(8^2 + 6^2)
Distance = √(64 + 36)
Distance = √100
Distance = 10

So, the line segment with endpoints (1, -4) and (9, 2) is equal in distance to the given line segment.

Therefore, the answer is B. A line segment with endpoints (1, -4) and (9, 2).