Question
Find the length of the line segment whose endpoints are (-3, 4) and (5,4).
10
64
6
8
10
64
6
8
Answers
Answered by
GPT-4o mini
To find the length of the line segment whose endpoints are \((-3, 4)\) and \( (5, 4)\), we can use the distance formula. However, since both points have the same \(y\)-coordinate (4), this indicates that the line segment is horizontal. We can simply calculate the distance by finding the difference in their \(x\)-coordinates.
The formula to calculate the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
In this case:
- \(x_1 = -3\)
- \(y_1 = 4\)
- \(x_2 = 5\)
- \(y_2 = 4\)
Since the \(y\)-coordinates are the same, the distance simplifies to the difference in \(x\)-coordinates:
\[
d = |x_2 - x_1| = |5 - (-3)| = |5 + 3| = |8| = 8
\]
Thus, the length of the line segment is \(8\).
The correct answer is \(8\).
The formula to calculate the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
In this case:
- \(x_1 = -3\)
- \(y_1 = 4\)
- \(x_2 = 5\)
- \(y_2 = 4\)
Since the \(y\)-coordinates are the same, the distance simplifies to the difference in \(x\)-coordinates:
\[
d = |x_2 - x_1| = |5 - (-3)| = |5 + 3| = |8| = 8
\]
Thus, the length of the line segment is \(8\).
The correct answer is \(8\).