Question

1. what is the distance formula used for calculating the distance between two points on a coordinate plane?

a. distance = (x₂ - x₁)² + (y₂ - y₁)²
b. distance = √((x₂ - x₁)² + (y₂ - y₁)²)
c. distance = √((x₂ + x₁)² + (y₂ + y₁)²)
d. distance = (x₂ - x₁) + (y₂ - y₁)

Explanation:

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ on a coordinate - plane is derived from the Pythagorean theorem. The horizontal distance between the points is $x_2 - x_1$ and the vertical distance is $y_2 - y_1$. The distance $d$ between the two points is the length of the hypotenuse of a right - triangle formed by these horizontal and vertical distances. By the Pythagorean theorem, $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Answer:

B. Distance = $\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$