Question
Find the length of the red line segment in the coordinate plane.
Which of the following statements are true:
Point 1 is (-2,1)
Point 2 is (4,3)
(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.
Skip to navigation
Which of the following statements are true:
Point 1 is (-2,1)
Point 2 is (4,3)
(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.
Skip to navigation
Answers
Answered by
GPT-4o mini
To find the length of the line segment between the two points, Point 1 \((-2, 1)\) and Point 2 \((4, 3)\), we will use the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Substituting the coordinates of the given points:
- \(x_1 = -2\)
- \(y_1 = 1\)
- \(x_2 = 4\)
- \(y_2 = 3\)
Calculating the differences:
\[
x_2 - x_1 = 4 - (-2) = 4 + 2 = 6
\]
\[
y_2 - y_1 = 3 - 1 = 2
\]
Now using the distance formula:
\[
d = \sqrt{(6)^2 + (2)^2} = \sqrt{36 + 4} = \sqrt{40}
\]
So, the length of the line segment is \(\sqrt{40}\) units.
Now let's evaluate the statements to determine which is true based on our calculation:
1. **The length is 40 units; find the sum of the x and y coordinates and square root the answer.**
- Incorrect. The length is not 40.
2. **The length is \(40^{1/2}\) units; find the sum of the vertical and horizontal distances squared and then take the square root.**
- Incorrect. This is a redundant way of stating it and is not clear.
3. **The length is \(\sqrt{40}\) units; find the sum of the vertical and horizontal distances squared and then take the square root.**
- True. This matches our calculation.
4. **The length is \(\sqrt{260}\); find the difference of the x coordinates and the difference of the y coordinates and subtract those differences.**
- Incorrect. The length is not \(\sqrt{260}\).
5. **The length is \(\sqrt{260}\); find the difference of the x coordinates and the difference of the y coordinates and subtract those differences.**
- Incorrect. Same reason as above.
6. **The length is 130; find the difference between the x and y coordinates and square it.**
- Incorrect. The length is not 130.
7. **The length is 130; find the difference between the x and y coordinates and square it.**
- Incorrect. Same reason as above.
The only true statement based on our calculation is statement **3**: **The length is \(\sqrt{40}\) units; find the sum of the vertical and horizontal distances squared and then take the square root.**
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Substituting the coordinates of the given points:
- \(x_1 = -2\)
- \(y_1 = 1\)
- \(x_2 = 4\)
- \(y_2 = 3\)
Calculating the differences:
\[
x_2 - x_1 = 4 - (-2) = 4 + 2 = 6
\]
\[
y_2 - y_1 = 3 - 1 = 2
\]
Now using the distance formula:
\[
d = \sqrt{(6)^2 + (2)^2} = \sqrt{36 + 4} = \sqrt{40}
\]
So, the length of the line segment is \(\sqrt{40}\) units.
Now let's evaluate the statements to determine which is true based on our calculation:
1. **The length is 40 units; find the sum of the x and y coordinates and square root the answer.**
- Incorrect. The length is not 40.
2. **The length is \(40^{1/2}\) units; find the sum of the vertical and horizontal distances squared and then take the square root.**
- Incorrect. This is a redundant way of stating it and is not clear.
3. **The length is \(\sqrt{40}\) units; find the sum of the vertical and horizontal distances squared and then take the square root.**
- True. This matches our calculation.
4. **The length is \(\sqrt{260}\); find the difference of the x coordinates and the difference of the y coordinates and subtract those differences.**
- Incorrect. The length is not \(\sqrt{260}\).
5. **The length is \(\sqrt{260}\); find the difference of the x coordinates and the difference of the y coordinates and subtract those differences.**
- Incorrect. Same reason as above.
6. **The length is 130; find the difference between the x and y coordinates and square it.**
- Incorrect. The length is not 130.
7. **The length is 130; find the difference between the x and y coordinates and square it.**
- Incorrect. Same reason as above.
The only true statement based on our calculation is statement **3**: **The length is \(\sqrt{40}\) units; find the sum of the vertical and horizontal distances squared and then take the square root.**