Question

find the distance between 2,3 and -4,-9

Answer 1

To find the distance between the points \( (2, 3) \) and \( (-4, -9) \), you can use the distance formula:

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

In this case, let \( (x_1, y_1) = (2, 3) \) and \( (x_2, y_2) = (-4, -9) \).

Now, substitute the values into the formula:

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

Calculate the differences:

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

Now calculate the squares:

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

Add them together:

\[
d = \sqrt{180}
\]

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

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

So, the distance between the two points is:

\[
6\sqrt{5}
\]