Asked by bruh no
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)
100
10
9.22
14
100
10
9.22
14
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 \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
For the points \((-1, 6)\) and \((5, -2)\), we have:
- \(x_1 = -1\)
- \(y_1 = 6\)
- \(x_2 = 5\)
- \(y_2 = -2\)
Now, plug in the values:
\[
d = \sqrt{(5 - (-1))^2 + (-2 - 6)^2}
\]
\[
d = \sqrt{(5 + 1)^2 + (-8)^2}
\]
\[
d = \sqrt{(6)^2 + (-8)^2}
\]
\[
d = \sqrt{36 + 64}
\]
\[
d = \sqrt{100}
\]
\[
d = 10
\]
So the distance between the points is \(10\).
The answer is **10**.
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
For the points \((-1, 6)\) and \((5, -2)\), we have:
- \(x_1 = -1\)
- \(y_1 = 6\)
- \(x_2 = 5\)
- \(y_2 = -2\)
Now, plug in the values:
\[
d = \sqrt{(5 - (-1))^2 + (-2 - 6)^2}
\]
\[
d = \sqrt{(5 + 1)^2 + (-8)^2}
\]
\[
d = \sqrt{(6)^2 + (-8)^2}
\]
\[
d = \sqrt{36 + 64}
\]
\[
d = \sqrt{100}
\]
\[
d = 10
\]
So the distance between the points is \(10\).
The answer is **10**.
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