Question 1: The length of the given line segment can be calculated using the distance formula:
√[(1-4)^2 + (11-7)^2]
= √[(-3)^2 + 4^2]
= √[9 + 16]
= √25
= 5
So, the length of the given line segment is 5.
Question 2: To find the line segment that is equal in distance to the given line segment, we need to calculate the lengths of the other line segments using the distance formula and compare them to 5.
A: √[(-6-2)^2 + (4-(-5))^2]
= √[(-8)^2 + 9^2]
= √[64 + 81]
= √145
≈ 12.04
B: √[(9-1)^2 + (2-(-4))^2]
= √[8^2 + 6^2]
= √[64 + 36]
= √100
= 10
C: √[(4-(-3))^2 + (5-1)^2]
= √[7^2 + 4^2]
= √[49 + 16]
= √65
≈ 8.06
D: √[(1-5)^2 + (6-3)^2]
= √[(-4)^2 + 3^2]
= √[16 + 9]
= √25
= 5
So, the line segment that is equal in distance to the given line segment is option D: A line segment with endpoints (5, 3) and (1, 6).