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Original Question
A (2,4) B(-2,-1) Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hund...Asked by Dino cat
A (2,-3)
B (5,5)
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.
(1 point)
8.54
73
7.62
11
B (5,5)
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.
(1 point)
8.54
73
7.62
11
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the distance between two points \( A(2, -3) \) and \( B(5, 5) \), we can use the distance formula, which is derived from the Pythagorean theorem:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Here, \( (x_1, y_1) \) are the coordinates of point \( A \) and \( (x_2, y_2) \) are the coordinates of point \( B \):
- \( x_1 = 2 \), \( y_1 = -3 \)
- \( x_2 = 5 \), \( y_2 = 5 \)
Now, plug the coordinates into the distance formula:
\[
d = \sqrt{(5 - 2)^2 + (5 - (-3))^2}
\]
\[
d = \sqrt{(3)^2 + (5 + 3)^2}
\]
\[
d = \sqrt{9 + 64}
\]
\[
d = \sqrt{73}
\]
Now, calculate \( \sqrt{73} \):
\[
\sqrt{73} \approx 8.54
\]
Thus, the length between points A and B is approximately **8.54**, rounded to the nearest hundredth.
The correct answer is:
**8.54**
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Here, \( (x_1, y_1) \) are the coordinates of point \( A \) and \( (x_2, y_2) \) are the coordinates of point \( B \):
- \( x_1 = 2 \), \( y_1 = -3 \)
- \( x_2 = 5 \), \( y_2 = 5 \)
Now, plug the coordinates into the distance formula:
\[
d = \sqrt{(5 - 2)^2 + (5 - (-3))^2}
\]
\[
d = \sqrt{(3)^2 + (5 + 3)^2}
\]
\[
d = \sqrt{9 + 64}
\]
\[
d = \sqrt{73}
\]
Now, calculate \( \sqrt{73} \):
\[
\sqrt{73} \approx 8.54
\]
Thus, the length between points A and B is approximately **8.54**, rounded to the nearest hundredth.
The correct answer is:
**8.54**
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