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Definition
The Distance Formula is a mathematical equation used to calculate the distance between two points in the coordinate plane.
This formula is derived from the Pythagorean Theorem, where the change in xxx and yyy represent the legs of a right triangle.
Summary
1. Derivation from the Pythagorean Theorem
- Visual representation of the distance between two points as the hypotenuse of a right triangle.
- Use of horizontal and vertical distances to form the legs:
- Applying the Pythagorean Theorem:
2. Applications
- Geometry: Measuring the length of a segment between two points.
- Analytic Geometry: Determining if a triangle is equilateral, isosceles, or right.
- Real-life Uses: Navigation, engineering, mapping, computer graphics.
3. Worked Examples
- Finding the distance between simple points like (0,0) and (3,4).
- Solving geometry problems involving midpoints, slopes, and distances.
4. Extensions
- In 3D space, the distance formula becomes:
- Can also be used to derive the equation of a circle:
Distance Formula Math Activities
This is a fantastic bundle which includes 10 activities with answer guides about Distance Formula. All our worksheets are completely editable so can be tailored for your curriculum and target audience.
Resource Examples
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Worksheets Activities Included
- Plot and Calculate
- Find the Missing Coordinate
- Compare Distances
- Distance on a Line
- Real-Life Coordinates
- Midpoint and Distance
- Using Distance Formula for a Circle
- Find the Diameter
- 3D Distance Extension
- Create & Solve