How do you find the distance between two points on a coordinate plane?

To find the distance between two points on a coordinate plane, you can use the distance formula, which is derived from the Pythagorean theorem. When given two points, ((x_1, y_1)) and ((x_2, y_2)), the distance between them can be calculated as follows:

1. Determine the horizontal and vertical differences between the points, which are (x_2 - x_1) for the x-coordinates and (y_2 - y_1) for the y-coordinates.
2. Square these differences: ((x_2 - x_1)²) and ((y_2 - y_1)²).
3. Add these squared values together: ((x_2 - x_1)² + (y_2 - y_1)²).
4. Finally, take the square root of that sum to find the straight-line distance: (\sqrt{(x_2 - x_1)² + (y_2 - y_1)²}).

Therefore, the correct formula effectively captures this geometric relationship, confirming that option C is indeed the appropriate choice. It provides a precise