To find the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a coordinate plane, you can use the distance formula, which is derived from the Pythagorean Theorem. The formula is:

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

Where:

• $(x_1, y_1)$ are the coordinates of the first point,
• $(x_2, y_2)$ are the coordinates of the second point,
• $d$ is the distance between the two points.

Example:

Find the distance between points $(3, 4)$ and $(7, 1)$.

$d = \sqrt{(7 - 3)^2 + (1 - 4)^2} = \sqrt{4^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5$

The distance between the two points is 5 units.

Would you like further explanation or more details?

Related Questions:

1. How is the distance formula related to the Pythagorean Theorem?
2. Can the distance formula be extended to 3D space?
3. What are some real-world applications of calculating distances between points?
4. How can the distance between points be found graphically?
5. How would you apply the formula to points with negative coordinates?

Tip:

If you often work with distances between points, it's helpful to visualize them as sides of a right triangle, with the distance being the hypotenuse.