Question
Triangles Online Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
13 of 1513 of 15 Items
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
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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