Question

find the distance between (2,3) and (-4, -9) round your answer to the nearest hundreth if nessacary

Answer 1

To find the distance between the points \((2, 3)\) and \((-4, -9)\), we 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:

\[
d = \sqrt{((-4) - 2)^2 + ((-9) - 3)^2}
\]

Calculating the differences:

\[
d = \sqrt{(-6)^2 + (-12)^2}
\]

Now, squaring the differences:

\[
d = \sqrt{36 + 144}
\]

Adding these values together:

\[
d = \sqrt{180}
\]

Now, we can simplify \(\sqrt{180}\):

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

Using a calculator to find the decimal value:

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

Rounding to the nearest hundredth:

\[
d \approx 13.42
\]

Thus, the distance between the two points is approximately **13.42**.