Distance in the Coordinate Plane

Distance Formula

The distance formula is used to find the length between two points in the xy-plane. It is derived from the Pythagorean Theorem and is fundamental in College Algebra and analytic geometry.

• Definition: The distance between two points and is given by:

• Application: This formula calculates the straight-line (Euclidean) distance between any two points in the plane.

Example Calculation

Find the distance between the points and .

• Step 1: Identify coordinates: and .

• Step 2: Substitute into the formula:

• Final Answer: The distance between and is approximately 18.97 units (rounded to the nearest hundredth).

Additional info:

• The distance formula is a direct application of the Pythagorean Theorem in the context of coordinate geometry.

• This concept is foundational for later topics such as equations of circles, midpoint formula, and analytic proofs.