Apply the Distance Formula

Question

Consider a line segment with endpoints (4, 7) and (1, 11).
Question 1
What is the length of the given line segment?
Responses
A 33
B 55
C 77
D 99
Question 2
Which line segment is equal in distance to the given line segment?
Responses
A A line segment with endpoints (−6, 4) and (2, −5).A line segment with endpoints (−6, 4) and (2, −5).
B A line segment with endpoints (1, −4) and (9, 2).A line segment with endpoints (1, −4) and (9, 2).
C A line segment with endpoints (−3, 1) and (4, 5).A line segment with endpoints (−3, 1) and (4, 5).
D A line segment with endpoints (5, 3) and (1, 6).A line segment with endpoints (5, 3) and (1, 6).
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Answer 1

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).