Question

Find the distance between the two points rounding to the nearest tenth (2,5) (-6,-3)

Answer 1

To find the distance between the two points \((2, 5)\) and \((-6, -3)\), we can use the distance formula:

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

Here, the coordinates are:
- \(x_1 = 2\), \(y_1 = 5\)
- \(x_2 = -6\), \(y_2 = -3\)

Now, substituting these values into the distance formula:

\[
d = \sqrt{((-6) - 2)^2 + ((-3) - 5)^2}
\]

Calculating the differences:

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

Calculating the squares:

\[
d = \sqrt{64 + 64}
\]
\[
d = \sqrt{128}
\]

Now we simplify \(\sqrt{128}\):

\[
\sqrt{128} = \sqrt{64 \times 2} = 8\sqrt{2}
\]

Now we can calculate \(8\sqrt{2}\):

Using \(\sqrt{2} \approx 1.414\):

\[
8\sqrt{2} \approx 8 \times 1.414 \approx 11.312
\]

Finally, rounding to the nearest tenth:

\[
d \approx 11.3
\]

Therefore, the distance between the two points is approximately \(11.3\).