Question
Triangles Online Practice
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Question
Apply the Pythagorean Theorem to find the length between (0, 6)
and (−3, −2)
. Round your answer to the nearest hundredth, if necessary.(1 point)
Responses
73
73
6.08
6.08
11
11
8.54
Answers
                                                    There are no human answers yet.
                                            
                
                    Answered by
            GPT-4o mini
            
    To find the distance between the points \((0, 6)\) and \((-3, -2)\), we can use the distance formula, which is derived from the Pythagorean Theorem. The formula is:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Here, \((x_1, y_1) = (0, 6)\) and \((x_2, y_2) = (-3, -2)\).
Now we substitute the coordinates into the formula:
1. Calculate \(x_2 - x_1\):
\[
-3 - 0 = -3
\]
2. Calculate \(y_2 - y_1\):
\[
-2 - 6 = -8
\]
3. Substitute these values into the distance formula:
\[
d = \sqrt{(-3)^2 + (-8)^2}
\]
\[
d = \sqrt{9 + 64}
\]
\[
d = \sqrt{73}
\]
Now, we can approximate \(\sqrt{73}\):
\[
\sqrt{73} \approx 8.54
\]
Thus, the answer, rounded to the nearest hundredth if necessary, is:
**8.54**
    
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Here, \((x_1, y_1) = (0, 6)\) and \((x_2, y_2) = (-3, -2)\).
Now we substitute the coordinates into the formula:
1. Calculate \(x_2 - x_1\):
\[
-3 - 0 = -3
\]
2. Calculate \(y_2 - y_1\):
\[
-2 - 6 = -8
\]
3. Substitute these values into the distance formula:
\[
d = \sqrt{(-3)^2 + (-8)^2}
\]
\[
d = \sqrt{9 + 64}
\]
\[
d = \sqrt{73}
\]
Now, we can approximate \(\sqrt{73}\):
\[
\sqrt{73} \approx 8.54
\]
Thus, the answer, rounded to the nearest hundredth if necessary, is:
**8.54**
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