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

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

• A. Distance = |x2 - x1| + |y2 - y1|
• B. Distance = √[(x1 + x2)² + (y1 + y2)²]
• C. Distance = √[(x2 - x1)² + (y2 - y1)²]
• D. Distance = (x2 - x1)² + (y2 - y1)²

Answer: (C)

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

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