Question

Distance and the Pythagorean Theorem Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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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:

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

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

Now, substitute the coordinates into the formula:

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

This simplifies to:

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

Next, we can simplify \(\sqrt{180}\):

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

Now, calculate the approximate value of \(6\sqrt{5}\):

\(\sqrt{5} \approx 2.236\)

So,

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

Rounding to the nearest hundredth, the distance is approximately:

\[
\boxed{13.42}
\]