Question

Find the distance between point
A
(
−
8
,

4
)
A(−8, 4) and
B
(
5
,

−
5
)
B(5, −5). Round your answer to the nearest tenth. Click Here for Help Video. Click Here if you would like to create a visual.

Answer 1

To find the distance between the points \( A(-8, 4) \) and \( B(5, -5) \), we can use the distance formula:

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

Here, \( (x_1, y_1) = (-8, 4) \) and \( (x_2, y_2) = (5, -5) \).

Now we can plug the coordinates into the formula:

1. Calculate \( x_2 - x_1 \):
\[
5 - (-8) = 5 + 8 = 13
\]

2. Calculate \( y_2 - y_1 \):
\[
-5 - 4 = -9
\]

3. Substitute these values into the distance formula:
\[
d = \sqrt{(13)^2 + (-9)^2} = \sqrt{169 + 81} = \sqrt{250}
\]

4. Simplify \( \sqrt{250} \):
\[
\sqrt{250} = \sqrt{25 \times 10} = 5\sqrt{10}
\]

5. Use a calculator to find \( 5\sqrt{10} \):
\[
5\sqrt{10} \approx 5 \times 3.162 = 15.81
\]

Rounding to the nearest tenth gives us:

\[
\text{Distance} \approx 15.8
\]

Thus, the distance between the points \( A \) and \( B \) is approximately **15.8**.