Question

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

52–√
5 square root of 2

5
5

6.5
6.5

25–√

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

Now, let's calculate the distance:

1. Calculate \( x_2 - x_1 \):
\[
7 - 2 = 5
\]

2. Calculate \( y_2 - y_1 \):
\[
8 - 3 = 5
\]

3. Substitute these values into the distance formula:
\[
d = \sqrt{(5)^2 + (5)^2} = \sqrt{25 + 25} = \sqrt{50}
\]

4. Simplify \( \sqrt{50} \):
\[
\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}
\]

Therefore, the distance between the points \( A(2, 3) \) and \( B(7, 8) \) is:

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