How do you find the distance between two points (x1, y1) and (x2, y2)?

How do you find the distance between two points (x1, y1) and (x2, y2)?

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

Answer: (B)

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a Cartesian coordinate system, you can use the distance formula, which is derived from the Pythagorean theorem. The correct formula is as follows: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] This formula calculates the straight-line distance between the two points. Each component \( (x_2 - x_1) \) and \( (y_2 - y_1) \) represents the horizontal and vertical distances between the two points respectively. Squaring these components ensures that the distance is non-negative, as distance cannot be negative, and then summing them follows the Pythagorean theorem where the distance forms the hypotenuse of a right triangle whose other sides are the differences in the x and y coordinates. The correct answer captures this relationship through the calculation, yielding the same result regardless of the order of the coordinates due to the properties of squaring and addition.

To find the distance between two points ((x_1, y_1)) and ((x_2, y_2)) in a Cartesian coordinate system, you can use the distance formula, which is derived from the Pythagorean theorem. The correct formula is as follows:

[

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

]

This formula calculates the straight-line distance between the two points. Each component ( (x_2 - x_1) ) and ( (y_2 - y_1) ) represents the horizontal and vertical distances between the two points respectively. Squaring these components ensures that the distance is non-negative, as distance cannot be negative, and then summing them follows the Pythagorean theorem where the distance forms the hypotenuse of a right triangle whose other sides are the differences in the x and y coordinates.

The correct answer captures this relationship through the calculation, yielding the same result regardless of the order of the coordinates due to the properties of squaring and addition.