Question

Find the distance between the points A(2,3) and B(7,8)(1 point)
Responses

2√5


6.5


5√2

5

Answer 1

To find the distance between the points A(2,3) and B(7,8), we can use the distance formula, which is given by:

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

Here, \( (x_1, y_1) = (2, 3) \) and \( (x_2, y_2) = (7, 8) \).

Now we can plug in the values:

\[
d = \sqrt{(7 - 2)^2 + (8 - 3)^2}
\]

Calculating the differences:

\[
d = \sqrt{(5)^2 + (5)^2}
\]

Now, square the differences:

\[
d = \sqrt{25 + 25}
\]

Combine the squares:

\[
d = \sqrt{50}
\]

We can simplify \(\sqrt{50}\):

\[
d = \sqrt{25 \times 2} = 5\sqrt{2}
\]

Thus, the distance between points A and B is:

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