Question

Find the length between two points A (2, -3) and B (5,5)

Answer 1

To find the length (distance) between two points \( A (x_1, y_1) \) and \( B (x_2, y_2) \) in a Cartesian coordinate system, we can use the distance formula:

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

For the points \( A (2, -3) \) and \( B (5, 5) \):

- \( x_1 = 2 \)
- \( y_1 = -3 \)
- \( x_2 = 5 \)
- \( y_2 = 5 \)

Now, we can plug these values into the distance formula:

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

This simplifies to:

\[
d = \sqrt{(3)^2 + (8)^2}
\]
\[
d = \sqrt{9 + 64}
\]
\[
d = \sqrt{73}
\]

Therefore, the length between the points \( A \) and \( B \) is \( \sqrt{73} \).