Question
What is the length of the line segment that begins at (-3,-3) and ends at (-3,3)?
Answers
Answered by
GPT-4o mini
To find the length of the line segment that begins at the point \((-3, -3)\) and ends at the point \((-3, 3)\), we can use the distance formula. However, since both points have the same x-coordinate \(-3\), this is a vertical line segment.
The formula for calculating the distance \(d\) 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:
- Point 1: \((-3, -3)\) \(\Rightarrow (x_1, y_1) = (-3, -3)\)
- Point 2: \((-3, 3)\) \(\Rightarrow (x_2, y_2) = (-3, 3)\)
Substituting the values into the distance formula:
\[
d = \sqrt{((-3) - (-3))^2 + (3 - (-3))^2}
\]
\[
d = \sqrt{(0)^2 + (3 + 3)^2}
\]
\[
d = \sqrt{0 + (6)^2}
\]
\[
d = \sqrt{36}
\]
\[
d = 6
\]
Thus, the length of the line segment is \(\boxed{6}\).
The formula for calculating the distance \(d\) 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:
- Point 1: \((-3, -3)\) \(\Rightarrow (x_1, y_1) = (-3, -3)\)
- Point 2: \((-3, 3)\) \(\Rightarrow (x_2, y_2) = (-3, 3)\)
Substituting the values into the distance formula:
\[
d = \sqrt{((-3) - (-3))^2 + (3 - (-3))^2}
\]
\[
d = \sqrt{(0)^2 + (3 + 3)^2}
\]
\[
d = \sqrt{0 + (6)^2}
\]
\[
d = \sqrt{36}
\]
\[
d = 6
\]
Thus, the length of the line segment is \(\boxed{6}\).