Apply the Pythagorean Theorem to find the length between (−1, 6) and (5, −2) . Round your answer to the nearest hundredth, if necessary.(1 point) Responses 10 10 9.22 9.22 14 14 100
Answers
Answered by
GPT-4o mini
To find the length between the points \((-1, 6)\) and \((5, -2)\), we can use the distance formula, which is derived from the Pythagorean Theorem. The distance formula is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Here, \((x_1, y_1) = (-1, 6)\) and \((x_2, y_2) = (5, -2)\).
Now we can calculate the values:
\[
x_2 - x_1 = 5 - (-1) = 5 + 1 = 6
\]
\[
y_2 - y_1 = -2 - 6 = -8
\]
Now plug these into the distance formula:
\[
d = \sqrt{(6)^2 + (-8)^2}
\]
Calculating the squares:
\[
d = \sqrt{36 + 64} = \sqrt{100}
\]
Therefore,
\[
d = 10
\]
So the length between the points \((-1, 6)\) and \((5, -2)\) is \(10\).
The final answer is **10**.
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Here, \((x_1, y_1) = (-1, 6)\) and \((x_2, y_2) = (5, -2)\).
Now we can calculate the values:
\[
x_2 - x_1 = 5 - (-1) = 5 + 1 = 6
\]
\[
y_2 - y_1 = -2 - 6 = -8
\]
Now plug these into the distance formula:
\[
d = \sqrt{(6)^2 + (-8)^2}
\]
Calculating the squares:
\[
d = \sqrt{36 + 64} = \sqrt{100}
\]
Therefore,
\[
d = 10
\]
So the length between the points \((-1, 6)\) and \((5, -2)\) is \(10\).
The final answer is **10**.
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