What is the distance formula in a coordinate plane?

What is the distance formula in a coordinate plane?

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

Answer: (C)

The distance formula in a coordinate plane is a mathematical expression used to determine the distance between two points, given their coordinates \((x_1, y_1)\) and \((x_2, y_2)\). The formula is derived from the Pythagorean theorem. When you consider a right triangle formed by these two points, the horizontal leg of the triangle represents the difference in the x-coordinates \((x_2 - x_1)\), while the vertical leg represents the difference in the y-coordinates \((y_2 - y_1)\). To find the distance between the two points, you apply the Pythagorean theorem: 1. Square the lengths of the legs: \((x_2 - x_1)^2\) for the horizontal leg and \((y_2 - y_1)^2\) for the vertical leg. 2. Add these two squares together: \((x_2 - x_1)^2 + (y_2 - y_1)^2\). 3. Take the square root of this sum to find the length of the hypotenuse, which represents the distance \(d\): \(d = \sqrt{(x_2

The distance formula in a coordinate plane is a mathematical expression used to determine the distance between two points, given their coordinates ((x_1, y_1)) and ((x_2, y_2)). The formula is derived from the Pythagorean theorem. When you consider a right triangle formed by these two points, the horizontal leg of the triangle represents the difference in the x-coordinates ((x_2 - x_1)), while the vertical leg represents the difference in the y-coordinates ((y_2 - y_1)).

To find the distance between the two points, you apply the Pythagorean theorem:

1. Square the lengths of the legs: ((x_2 - x_1)^2) for the horizontal leg and ((y_2 - y_1)^2) for the vertical leg.

2. Add these two squares together: ((x_2 - x_1)^2 + (y_2 - y_1)^2).

3. Take the square root of this sum to find the length of the hypotenuse, which represents the distance (d): (d = \sqrt{(x_2