The distance between two points is the length of the straight line segment that connects them. We can find this distance using the distance formula, which is based on the Pythagorean theorem. This formula helps us calculate the distance on a coordinate plane given the coordinates of the two points. Understanding this concept is super useful in geometry, navigation, and even computer graphics!
Imagine you have two points, A and B, on a graph. Point A has coordinates (x₁, y₁) and point B has coordinates (x₂, y₂). The distance formula helps us figure out the straight-line distance between them. Think of it as drawing a right triangle where the distance between the points is the hypotenuse. Let's dive into the formula!
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Coordinate Plane | a. The square root of the sum of the squares of the differences in x and y coordinates. |
| 2. Distance Formula | b. A plane formed by two perpendicular number lines, called axes. |
| 3. x-coordinate | c. The horizontal distance of a point from the origin. |
| 4. y-coordinate | d. The vertical distance of a point from the origin. |
| 5. Distance | e. The length between two points. |
Complete the paragraph using the words: Pythagorean, coordinates, distance, formula, plane.
The _______ between two points on a coordinate _______ can be found using the _______ _______. This _______ is derived from the _______ theorem and uses the _______ of the two points.
Explain in your own words how the distance formula relates to the Pythagorean theorem. Provide an example to illustrate your explanation.
Please log in to post your answer.
Log InEarn 2 Points for answering. If your answer is selected as the best, you'll get +20 Points! 🚀