To find the length of a line segment in the coordinate plane, we can use the distance formula, which is derived from the Pythagorean theorem. The formula for the distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Let's evaluate the statements one by one to determine which are true:
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The length is 130; find the difference between the x and y coordinates and square it.
- This statement is not correct because the distance involves squaring both differences (vertical and horizontal) and adding them, not just taking the difference of the x and y coordinates.
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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 is also incorrect because it misrepresents how to calculate the distance.
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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 could potentially be true if indeed \( d = \sqrt{40} \), but we would need the specific coordinates to know if this is the correct calculation.
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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 is incorrect because it misrepresents the calculation for the distance. The correct operation is to square the differences and then add them, not subtract them.
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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 is also inaccurate because, as stated, the process is incorrect.
Without specific coordinates, we cannot definitively determine the length or correctness of the distance calculations. Please provide the coordinates of the endpoints of the red line segment for further evaluation.