Question

How do I calculate the distance between the points (3,2) and (2,4) in a coordinate plane?

Answer 1

To calculate the distance between two points in a coordinate plane, you can use the distance formula. The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:

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

For the points \( (3, 2) \) and \( (2, 4) \):

- Let \( (x_1, y_1) = (3, 2) \)
- Let \( (x_2, y_2) = (2, 4) \)

Now, substitute the coordinates into the formula:

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

Calculating the differences:

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

Now calculate the squares:

\[
d = \sqrt{1 + 4}
\]

Adding them together:

\[
d = \sqrt{5}
\]

Therefore, the distance between the points \( (3, 2) \) and \( (2, 4) \) is \( \sqrt{5} \).