Question

Find the distance between (2, 3) and (−4, −9). Round your answer to the nearest hundredth, if necessary.(1 point)

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 \((x_2, y_2) = (-4, -9)\).

Now, we can plug in the coordinates into the formula:

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

Calculating each part:

1. Calculate \(x_2 - x_1\):
\[
-4 - 2 = -6
\]
So, \((-6)^2 = 36\).

2. Calculate \(y_2 - y_1\):
\[
-9 - 3 = -12
\]
So, \((-12)^2 = 144\).

Now plug these into the distance formula:

\[
d = \sqrt{36 + 144} = \sqrt{180}
\]

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

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

Using a calculator to get the numerical value:

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

Rounding to the nearest hundredth, we get:

\[
d \approx 13.42
\]

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