Find the distance between and . Round your answer to the

nearest hundredth, if necessary. (1 point)
(−8, − 3) (−2, − 5)

1 answer

To find the distance between the two points \((-8, -3)\) and \((-2, -5)\), you can use the distance formula:

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

Here, we have:

  • \((x_1, y_1) = (-8, -3)\)
  • \((x_2, y_2) = (-2, -5)\)

Now, substituting the coordinates into the formula:

\[ d = \sqrt{((-2) - (-8))^2 + ((-5) - (-3))^2} \]

Calculating the differences:

\[ d = \sqrt{(-2 + 8)^2 + (-5 + 3)^2} \] \[ d = \sqrt{(6)^2 + (-2)^2} \] \[ d = \sqrt{36 + 4} \] \[ d = \sqrt{40} \] \[ d = \sqrt{4 \times 10} = 2\sqrt{10} \]

Calculating \(2\sqrt{10}\):

\[ \sqrt{10} \approx 3.1623 \] So, \[ 2\sqrt{10} \approx 2 \times 3.1623 \approx 6.3246 \]

Rounding to the nearest hundredth, we get:

\[ \approx 6.32 \]

Thus, the distance between the points \((-8, -3)\) and \((-2, -5)\) is approximately \(\boxed{6.32}\).