Question

Find the distance between (2, 3)
and (−4, −9)
. Round your answer to the nearest hundredth, if necessary.

Answer 1

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

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

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

Plugging in the values:

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

Calculating the differences:

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

Calculating the squares:

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

Adding the squares:

\[
d = \sqrt{180}
\]

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

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

To get the numerical value, we calculate \(6\sqrt{5}\). Since \(\sqrt{5} \approx 2.236\):

\[
d \approx 6 \times 2.236 = 13.416
\]

Rounding this to the nearest hundredth gives:

\[
d \approx 13.42
\]

Thus, the distance between the points \((2, 3)\) and \((-4, -9)\) is approximately \( \boxed{13.42} \).