Question

Find the distance between Point A and Point B. Enter your answer in the box.A coordinate plane with two points. Point A has coordinates 2 comma 1 and point B has coordinates 5 comma 5. units

Answer 1

To find the distance between two points \( A(2, 1) \) and \( B(5, 5) \) in a coordinate plane, we can use the distance formula:

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

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

Here, \( (x_1, y_1) = (2, 1) \) and \( (x_2, y_2) = (5, 5) \).

Now, substituting the coordinates into the formula:

\[
d = \sqrt{(5 - 2)^2 + (5 - 1)^2}
\]

Calculating the differences:

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

Calculating the squares:

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

Adding the squares:

\[
d = \sqrt{25}
\]

Finally, taking the square root:

\[
d = 5
\]

Thus, the distance between Point A and Point B is \( \boxed{5} \) units.