Question

what is the distance formula used for calculating the distance between two points on a coordinate plane?
a. distance = (x₂ - x₁) + (y₂ - y₁)
b. distance = √(x₂ + x₁)² + (y₂ + y₁)²
c. distance = √(x₂ - x₁)² + (y₂ - y₁)²
d. distance = (x₂ - x₁)² + (y₂ - y₁)²

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, where the horizontal difference $(x_2 - x_1)$ and vertical difference $(y_2 - y_1)$ form the legs of a right triangle, and the distance is the hypotenuse. This matches option c.

Answer:

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