Distance and the Pythagorean Theorem Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items

Question
Find the distance between (−8, −3)
and (−2, −5)
. Round your answer to the nearest hundredth, if necessary.(1 point)
units

Answer 1

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

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

where \((x_1, y_1) = (-8, -3)\) and \((x_2, y_2) = (-2, -5)\).

Now we can plug in the values:

1. Calculate the differences:

   • \(x_2 - x_1 = -2 - (-8) = -2 + 8 = 6\)
   • \(y_2 - y_1 = -5 - (-3) = -5 + 3 = -2\)

2. Substitute these values into the distance formula: \[ d = \sqrt{(6)^2 + (-2)^2} = \sqrt{36 + 4} = \sqrt{40} \]

3. Simplify the square root: \[ \sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10} \]

4. Now, calculate the approximate value of \(2\sqrt{10}\): \[ \sqrt{10} \approx 3.162 \quad \Rightarrow \quad 2\sqrt{10} \approx 2 \times 3.162 \approx 6.324 \]

Finally, rounding \(6.324\) to the nearest hundredth gives \(6.32\).

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