Apply the Pythagorean Theorem to find the length between (−1, 6) and (5, −2)

Question

. Round your answer to the nearest hundredth, if necessary.(1 point)
Responses

9.22
9.22
100
100
14
14
10

Answer 1

To find the length between the points \((-1, 6)\) and \( (5, -2)\), we can use the Pythagorean Theorem, which in the context of a coordinate plane gives us the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Where \((x_1, y_1) = (-1, 6)\) and \((x_2, y_2) = (5, -2)\).

Plugging the coordinates into the formula:

1. Calculate \(x_2 - x_1\):

\[ 5 - (-1) = 5 + 1 = 6 \]

2. Calculate \(y_2 - y_1\):

\[ -2 - 6 = -8 \]

3. Plugging these values into the distance formula:

\[ d = \sqrt{(6)^2 + (-8)^2} \]

4. Calculate \((6)^2\) and \((-8)^2\):

\[ (6)^2 = 36 \] \[ (-8)^2 = 64 \]

5. Add the squares:

\[ 36 + 64 = 100 \]

6. Take the square root:

\[ d = \sqrt{100} = 10 \]

So, the length between the points \((-1, 6)\) and \( (5, -2)\) is \(10\).

Thus, the answer is:

10