Question

Find the distance between the points left parenthesis negative 1 comma 2 right parenthesis and left parenthesis 3 comma 4 right parenthesis. Express your answer in simplest radical form.
(1 point)
Responses

2 Start Root 5 End Root
Image with alt text: 2 Start Root 5 End Root

Start Root 8 End Root
Image with alt text: Start Root 8 End Root

Start Root 20 End Root
Image with alt text: Start Root 20 End Root

2 Start Root 2 End Root
Image with alt text: 2 Start Root 2 End Root

Answer 1

To find the distance between the points \((-1, 2)\) and \((3, 4)\), we can use the distance formula:

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

Here, \((x_1, y_1) = (-1, 2)\) and \((x_2, y_2) = (3, 4)\).

Now, we can plug in the values:

\[
d = \sqrt{(3 - (-1))^2 + (4 - 2)^2}
\]

Calculating the differences:

\[
d = \sqrt{(3 + 1)^2 + (4 - 2)^2} = \sqrt{(4)^2 + (2)^2}
\]

Now, square the differences:

\[
d = \sqrt{16 + 4} = \sqrt{20}
\]

Now, simplify \(\sqrt{20}\):

\[
\sqrt{20} = \sqrt{4 \cdot 5} = 2\sqrt{5}
\]

Thus, the distance between the points \((-1, 2)\) and \((3, 4)\) is:

\[
\boxed{2\sqrt{5}}
\]