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

Answer 1

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

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Here, \( (x_1, y_1) = (4, 7) \) and \( (x_2, y_2) = (1, 11) \).

Calculating the differences:

\[
x_2 - x_1 = 1 - 4 = -3
\]
\[
y_2 - y_1 = 11 - 7 = 4
\]

Now, substituting these values into the distance formula:

\[
d = \sqrt{(-3)^2 + (4)^2}
\]
\[
d = \sqrt{9 + 16}
\]
\[
d = \sqrt{25}
\]
\[
d = 5
\]

So the length of the line segment is \(5\). However, this value does not match any of the options provided (A: 33, B: 55, C: 77, D: 99), indicating an error in the question or answer options.

Please double-check the endpoints or answer choices provided.