Question
Find the length of the red line segment in the coordinate plane.
Which of the following statements are true:
(1 point)
Responses
The length is 40 units; find the sum of the x and y coordinates and square root the answer.
The length is 40 units; find the sum of the x and y coordinates and square root the answer.
The length is 40−−√
units; find the sum of the vertical and horizontal distances squared and then take the square root.
The length is square root of 40 units; find the sum of the vertical and horizontal distances squared and then take the square root.
The length is 260−−−√
; find the difference of the x coordinates and the difference of the y coordinates and subtract those differences.
The length is square root of 260 ; find the difference of the x coordinates and the difference of the y coordinates and subtract those differences.
The length is 130; find the difference between the x and y coordinates and square it.
The length is 130; find the difference between the x and y coordinates and square it.
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Which of the following statements are true:
(1 point)
Responses
The length is 40 units; find the sum of the x and y coordinates and square root the answer.
The length is 40 units; find the sum of the x and y coordinates and square root the answer.
The length is 40−−√
units; find the sum of the vertical and horizontal distances squared and then take the square root.
The length is square root of 40 units; find the sum of the vertical and horizontal distances squared and then take the square root.
The length is 260−−−√
; find the difference of the x coordinates and the difference of the y coordinates and subtract those differences.
The length is square root of 260 ; find the difference of the x coordinates and the difference of the y coordinates and subtract those differences.
The length is 130; find the difference between the x and y coordinates and square it.
The length is 130; find the difference between the x and y coordinates and square it.
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Answers
Answered by
GPT-4o mini
To find the length of a line segment in the coordinate plane, we use the distance formula, which is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Here, \(d\) is the distance (length of the line segment), \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two endpoints of the line segment.
Let's evaluate the statements provided:
1. **The length is 40 units; find the sum of the x and y coordinates and square root the answer.**
- This statement is incorrect. The length isn't simply the sum of coordinates.
2. **The length is 40−−√ units; find the sum of the vertical and horizontal distances squared and then take the square root.**
- This is conceptually correct as it follows the proper method of calculating distance (using the Pythagorean theorem). However, if the distance came out to exactly \(40\), then the length being represented as \(40^{1/2}\) is false.
3. **The length is square root of 40 units; find the sum of the vertical and horizontal distances squared and then take the square root.**
- This is essentially the same as the previous statement but is mathematically invalid as the distance length should not equal \(\sqrt{40}\).
4. **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 incorrect regarding the interpretation. Correctly, according to the distance formula, you would add the squares and take the square root rather than subtracting differences.
5. **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 incorrect as it does not align with the distance formula.
6. **The length is 130; find the difference between the x and y coordinates and square it.**
- Incorrect, as this does not align with distance calculation.
7. **The length is 130; find the difference between the x and y coordinates and square it.**
- Again, incorrect for the same reason as above.
Overall, you would typically need the coordinates of the endpoints of the line segment to properly evaluate these lengths. None of the statements accurately represent the correct calculation for the lengths in the coordinate plane. If you provide specific coordinates, I could calculate the exact length for you.
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Here, \(d\) is the distance (length of the line segment), \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two endpoints of the line segment.
Let's evaluate the statements provided:
1. **The length is 40 units; find the sum of the x and y coordinates and square root the answer.**
- This statement is incorrect. The length isn't simply the sum of coordinates.
2. **The length is 40−−√ units; find the sum of the vertical and horizontal distances squared and then take the square root.**
- This is conceptually correct as it follows the proper method of calculating distance (using the Pythagorean theorem). However, if the distance came out to exactly \(40\), then the length being represented as \(40^{1/2}\) is false.
3. **The length is square root of 40 units; find the sum of the vertical and horizontal distances squared and then take the square root.**
- This is essentially the same as the previous statement but is mathematically invalid as the distance length should not equal \(\sqrt{40}\).
4. **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 incorrect regarding the interpretation. Correctly, according to the distance formula, you would add the squares and take the square root rather than subtracting differences.
5. **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 incorrect as it does not align with the distance formula.
6. **The length is 130; find the difference between the x and y coordinates and square it.**
- Incorrect, as this does not align with distance calculation.
7. **The length is 130; find the difference between the x and y coordinates and square it.**
- Again, incorrect for the same reason as above.
Overall, you would typically need the coordinates of the endpoints of the line segment to properly evaluate these lengths. None of the statements accurately represent the correct calculation for the lengths in the coordinate plane. If you provide specific coordinates, I could calculate the exact length for you.