Question

Find the distance between (2, 3) and (-4, -9). Round your answer to the nearest hundreth

Answer 1

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

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

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

Now, let's calculate the difference in the x-coordinates and the y-coordinates:

\[
x_2 - x_1 = -4 - 2 = -6
\]
\[
y_2 - y_1 = -9 - 3 = -12
\]

Next, we square these differences:

\[
(-6)^2 = 36
\]
\[
(-12)^2 = 144
\]

Now, we can plug these values into the distance formula:

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

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

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

Next, we calculate \(6\sqrt{5}\) to the nearest hundredth. We know that:

\[
\sqrt{5} \approx 2.236
\]
So,

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

Finally, rounding this to the nearest hundredth, we get:

\[
\boxed{13.42}
\]

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