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 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 compute the distance step by step:

1. Calculate the differences in the x-coordinates and y-coordinates:
- \(x_2 - x_1 = -4 - 2 = -6\)
- \(y_2 - y_1 = -9 - 3 = -12\)

2. Square these differences:
- \((-6)^2 = 36\)
- \((-12)^2 = 144\)

3. Sum the squares:
\[
36 + 144 = 180
\]

4. Take the square root of the sum:
\[
d = \sqrt{180}
\]

5. Simplify \(\sqrt{180}\):
\[
\sqrt{180} = \sqrt{36 \times 5} = 6\sqrt{5}
\]

6. Now we approximate \(\sqrt{5}\) which is approximately \(2.236\):
\[
6\sqrt{5} \approx 6 \times 2.236 = 13.416
\]

7. Therefore, rounding to the nearest hundredth, the distance is:
\[
\boxed{13.42}
\]