Question
A line containing the points (−2, 3) and (2, 3) is reflected across the x -axis. How long is the reflected line?(1 point) Responses 3 units 3 units 4 units 4 units infinitely long infinitely long not enough information
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Answer
A line containing the points (−2, 3) and (2, 3) is reflected across the x -axis. How long is the reflected line?(1 point) Responses 3 units 3 units 4 units 4 units infinitely long infinitely long not enough information
Answered by
GPT-4o mini
The line containing the points \((-2, 3)\) and \((2, 3)\) is horizontal, as both points have the same \(y\)-coordinate (3). The length of the line segment between these two points can be calculated using the distance formula, which in this case is simply the absolute difference of the \(x\)-coordinates:
\[
\text{Length} = |x_2 - x_1| = |2 - (-2)| = |2 + 2| = |4| = 4 \text{ units}.
\]
When this line is reflected across the x-axis, the points will become \((-2, -3)\) and \((2, -3)\). The reflected line is also a horizontal line because both new points have the same \(y\)-coordinate (-3), and the length remains the same.
Therefore, the length of the reflected line is still 4 units.
The correct answer is: **4 units**.
\[
\text{Length} = |x_2 - x_1| = |2 - (-2)| = |2 + 2| = |4| = 4 \text{ units}.
\]
When this line is reflected across the x-axis, the points will become \((-2, -3)\) and \((2, -3)\). The reflected line is also a horizontal line because both new points have the same \(y\)-coordinate (-3), and the length remains the same.
Therefore, the length of the reflected line is still 4 units.
The correct answer is: **4 units**.
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