What does the formula d = √(x2 - x1)² + (y2 - y1)² represent?

What does the formula d = √(x2 - x1)² + (y2 - y1)² represent?

• A. Area of a triangle
• B. Distance between two points
• C. Perimeter of a rectangle
• D. Volume of a cylinder

Answer: (B)

The formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \) calculates the distance between two points in a Cartesian coordinate system, where \( (x_1, y_1) \) and \( (x_2, y_2) \) represent the coordinates of the two points. This formula is derived from the Pythagorean theorem, which relates the lengths of the sides of a right triangle to the length of the hypotenuse. In this context, the differences in the x-coordinates \( (x_2 - x_1) \) and the differences in the y-coordinates \( (y_2 - y_1) \) serve as the two perpendicular sides of a triangle, with the distance \( d \) representing the hypotenuse. By squaring these differences, summing them, and then taking the square root, the formula effectively gives you the straight-line distance between the two points. Other options refer to different geometric concepts. The area of a triangle involves base and height, the perimeter of a rectangle concerns the sum of all its sides, and the volume of a cylinder relates to the space it

The formula ( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ) calculates the distance between two points in a Cartesian coordinate system, where ( (x_1, y_1) ) and ( (x_2, y_2) ) represent the coordinates of the two points. This formula is derived from the Pythagorean theorem, which relates the lengths of the sides of a right triangle to the length of the hypotenuse. In this context, the differences in the x-coordinates ( (x_2 - x_1) ) and the differences in the y-coordinates ( (y_2 - y_1) ) serve as the two perpendicular sides of a triangle, with the distance ( d ) representing the hypotenuse. By squaring these differences, summing them, and then taking the square root, the formula effectively gives you the straight-line distance between the two points.

Other options refer to different geometric concepts. The area of a triangle involves base and height, the perimeter of a rectangle concerns the sum of all its sides, and the volume of a cylinder relates to the space it