Question

Find the distance between the points A(2, 3) and B(7, 8). Your answer should be in simplest radical form.(1 point)
Responses

25–√
2 square root of 5

52–√
5 square root of 2

5
5

6.5

Answer 1

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

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

Here, \( (x_1, y_1) \) are the coordinates of point A, and \( (x_2, y_2) \) are the coordinates of point B.

Substituting the coordinates of points A and B into the formula:

- \( x_1 = 2 \)
- \( y_1 = 3 \)
- \( x_2 = 7 \)
- \( y_2 = 8 \)

Plugging in these values:

\[
d = \sqrt{(7 - 2)^2 + (8 - 3)^2}
\]
\[
d = \sqrt{(5)^2 + (5)^2}
\]
\[
d = \sqrt{25 + 25}
\]
\[
d = \sqrt{50}
\]

Now, we can simplify \( \sqrt{50} \):

\[
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}
\]

Thus, the distance between points A and B is \( 5\sqrt{2} \).

Therefore, the answer in simplest radical form is:

**5√2**