Question

find the distance between 2,3 and -4,-9 round answer to nearest hundreth if necessary

Answer 1

To find the distance between the points \((2, 3)\) and \((-4, -9)\), you can use the distance formula:

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

Here, \((x_1, y_1) = (2, 3)\) and \((x_2, y_2) = (-4, -9)\).

Plugging in the values:

\[
d = \sqrt{((-4) - 2)^2 + ((-9) - 3)^2}
\]
\[
d = \sqrt{(-6)^2 + (-12)^2}
\]
\[
d = \sqrt{36 + 144}
\]
\[
d = \sqrt{180}
\]

Now, simplifying \(\sqrt{180}\):

\[
\sqrt{180} = \sqrt{36 \times 5} = 6\sqrt{5}
\]

To get a decimal approximation:

\[
\sqrt{5} \approx 2.236
\]
\[
6\sqrt{5} \approx 6 \times 2.236 \approx 13.416
\]

Rounded to the nearest hundredth, the distance is:

\[
\approx 13.42
\]

So, the distance between the points \((2, 3)\) and \((-4, -9)\) is approximately **13.42**.