To determine the length of line segment \( BC \) after undergoing a reflection over the y-axis, we need to use the coordinates of points \( B \) and \( C \). However, since you did not provide specific coordinates for points \( B \) and \( C \), I will explain the general process to find the length of the segment.
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Find the Coordinates of Points B and C: Let's assume that the coordinates of points are:
- Point \( B \) has coordinates \( (x_1, y_1) \)
- Point \( C \) has coordinates \( (x_2, y_2) \)
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Reflect Points Over the Y-Axis:
- The reflection of point \( B \) over the y-axis will be \( B' = (-x_1, y_1) \)
- The reflection of point \( C \) over the y-axis will be \( C' = (-x_2, y_2) \)
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Calculate the Length of Segment \( B'C' \): The formula for the length of a line segment given two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is: \[ \text{Length} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting the coordinates of the reflected points, the formula becomes: \[ \text{Length} = \sqrt{((-x_2) - (-x_1))^2 + (y_2 - y_1)^2} = \sqrt{(-x_2 + x_1)^2 + (y_2 - y_1)^2} \] This simplifies to: \[ \text{Length} = \sqrt{(x_1 - x_2)^2 + (y_2 - y_1)^2} \]
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Final Result: The length of segment \( BC \) remains the same before and after the reflection over the y-axis, since reflection does not change the distance between two points.
So, if you simply need the length of \( BC \), you can compute it directly from the coordinates of \( B \) and \( C \) using the distance formula stated above. If you provide specific coordinates, I can calculate it for you.