Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary.

(−5, −1), (7, −8)

Question 3 options:

4.4

9.2

12.6

13.9

1 answer

To find the distance between the points \((-5, -1)\) and \((7, -8)\), we can use the distance formula:

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

where \((x_1, y_1)\) are the coordinates of the first point, and \((x_2, y_2)\) are the coordinates of the second point.

Plugging in the coordinates:

  • \((x_1, y_1) = (-5, -1)\)
  • \((x_2, y_2) = (7, -8)\)

Now substitute into the formula:

\[ d = \sqrt{(7 - (-5))^2 + (-8 - (-1))^2} \]

Calculating the differences:

\[ 7 - (-5) = 7 + 5 = 12 \] \[ -8 - (-1) = -8 + 1 = -7 \]

Now substitute these back into the distance formula:

\[ d = \sqrt{(12)^2 + (-7)^2} \] \[ d = \sqrt{144 + 49} \] \[ d = \sqrt{193} \]

Now, we need to calculate \(\sqrt{193}\):

\[ \sqrt{193} \approx 13.9 \]

Thus, the distance between the points \((-5, -1)\) and \((7, -8)\) is approximately 13.9.

So the answer is:

13.9