Apply the Pythagorean Theorem to find the length between (−1, 6) and (5, −2) . Round your answer to the nearest hundredth, if necessary.

1. 10
2. 9.22
3. 100
4. 14

1 answer

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:

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

Plugging in the coordinates of the points:

  • \((x_1, y_1) = (-1, 6)\)
  • \((x_2, y_2) = (5, -2)\)

We first calculate the differences:

\[ x_2 - x_1 = 5 - (-1) = 5 + 1 = 6 \] \[ y_2 - y_1 = -2 - 6 = -8 \]

Now, we can plug these values into the distance formula:

\[ d = \sqrt{(6)^2 + (-8)^2} \] \[ d = \sqrt{36 + 64} \] \[ d = \sqrt{100} \] \[ d = 10 \]

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

So the answer is 1. 10.