The distance formula is used to calculate the distance between two points in a coordinate plane. If you have two points $(x_1, y_1)$ and $(x_2, y_2)$, the distance $d$ between them is given by the formula:

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

Steps to Use the Distance Formula:

1. Find the difference between the x-coordinates: $x_2 - x_1$.
2. Find the difference between the y-coordinates: $y_2 - y_1$.
3. Square both differences: $(x_2 - x_1)^2$ and $(y_2 - y_1)^2$.
4. Add the squared differences together.
5. Take the square root of the sum to get the distance.

Example:

For points $A(2, 3)$ and $B(5, 7)$:

$d = \sqrt{(5 - 2)^2 + (7 - 3)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$

The distance between points $A$ and $B$ is 5 units.

Would you like more details or have any questions?

Related Questions:

1. How do you apply the distance formula in three-dimensional space?
2. Can the distance formula be used to find the length of a diagonal in a rectangle?
3. How is the distance formula related to the Pythagorean theorem?
4. What is the distance between two points on a circle?
5. How can the distance formula be applied in real-world scenarios?

Tip:

Always double-check the coordinates you substitute into the formula to avoid calculation errors.