Question

Find the distance between (2, 3) and (–1, 7).

5
√7
25
none of the answer choices

Answer 1

To find the distance between the points \((2, 3)\) and \((-1, 7)\), we can use the distance formula:

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

Here, \((x_1, y_1) = (2, 3)\) and \((x_2, y_2) = (-1, 7)\).

Now, substitute the coordinates into the formula:

\[
d = \sqrt{((-1) - 2)^2 + (7 - 3)^2}
\]

Calculating the differences gives:

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

Now calculate the squares:

\[
d = \sqrt{9 + 16}
\]

Add the values:

\[
d = \sqrt{25}
\]

Finally, take the square root:

\[
d = 5
\]

Thus, the distance between the points \((2, 3)\) and \((-1, 7)\) is \(5\).

The correct answer is \(5\).