To determine the correct statement regarding the length of the red line segment in the coordinate plane, we must first recall the formula for the distance between two points in the Cartesian coordinate system:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two endpoints of the line segment.
Since we do not have specific coordinates given in your question, I will analyze the provided statements based on common scenarios.
Analyzing the statements:
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The length is \( \sqrt{40} \) units; find the sum of the vertical and horizontal distances squared and then take the square root.
- This statement is true if the calculated values for the squared distances add up to 40.
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The length is \( \sqrt{260} \); find the difference of the x coordinates and the difference of the y coordinates and subtract those differences.
- This statement is misleading; the lenght cannot be obtained by merely subtracting the differences of the coordinates. This is incorrect.
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The length is 40 units; find the sum of the x and y coordinates and square root the answer.
- This statement doesn't reflect the correct way to calculate the distance between two points. This is incorrect.
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The length is 130; find the difference between the x and y coordinates and square it.
- Again, this method does not properly compute the distance. This is incorrect.
From this evaluation, the first statement could be correct depending on the actual values used upon applying the distance formula.
Without the actual coordinates of the endpoints of the segment, I cannot definitively tell you the correct length or which statements are true. However, statement 1 is most aligned with the correct method of finding the distance using the distance formula.
If you happen to have specific coordinates of the endpoints or further context, I can provide a more accurate evaluation.