Question

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

2 Start Root 10 End Root
Image with alt text: 2 Start Root 10 End Root

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

2 Start Root 3 End Root
Image with alt text: 2 Start Root 3 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 \((4, 3)\) and \((2, -1)\), we use the distance formula:

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

Where:
- \((x_1, y_1) = (4, 3)\)
- \((x_2, y_2) = (2, -1)\)

Now we can plug in the values:

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

Calculating the differences:

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

Calculating the squares:

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

Adding the results:

\[
d = \sqrt{20}
\]

We can simplify \(\sqrt{20}\):

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

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

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