Question

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

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 the coordinates into the formula:

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

Calculating each part:

1. \( (-4 - 2) = -6 \)
2. \( (-9 - 3) = -12 \)

Now squaring these differences:

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

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

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

Now, using a calculator to find the decimal value:

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

Finally, rounding to the nearest hundredth:

\[
\approx 13.42
\]

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