DISTANCE FORMULA
Definition of Distance Formula
The formula 
, which is used to find the distance between two points (x1, y1) and (x2, y2), is called the Distance Formula.
Examples of Distance Formula
The distance between the points (1, 3) and (2, 5) is
Solved Example on Distance Formula
What is the distance between the points A (4, 6) and B (- 2, - 2)?
Choices:
A. 10
B. 6
C. 8
D. 4
Correct Answer: A
Solution:
Step 1: (x1, y1) and (x2, y2) = (- 2, - 2)
Step 2: Distance between the two points can be found using the distance formula 
.
Step 3: So, AB = 
= 10 units.
Related Terms for Distance Formula
Point
Distance
Formula
Quick Summary
- The distance formula calculates the length of a line segment between two points.
- It uses the coordinates of the two points (x1, y1) and (x2, y2).
- The formula is derived from the Pythagorean theorem.
⚠️ Common Mistakes
- Incorrectly identifying x1, y1, x2, y2.
- Forgetting to square the differences.
- Not taking the square root at the end.
🌍 Real-World Uses
- Calculating the shortest flight path distance between two cities given their GPS coordinates.
- Determining the length of a cable needed to connect two points in construction or surveying.
- Estimating the distance between two objects detected by radar or sonar systems, like ships or aircraft.
📋 Standards Alignment
CCSS.MATH.CONTENT.8.G.B.7CCSS.MATH.CONTENT.HSG.GPE.B.7
🔗 Related Links
🍎 Teacher Insights
Emphasize the connection to the Pythagorean theorem. Use visual aids to demonstrate the formula. Provide ample practice problems with varying levels of difficulty.🎓 Prerequisites
- Pythagorean Theorem
- Coordinate Plane
- Square Roots
Check Your Knowledge
Q1: What is the distance between the points (1, 2) and (4, 6)?
Q2: The distance between points A(0,0) and B(3,4) is
Frequently Asked Questions
Q: Can the distance be negative?
A: No, distance is always a non-negative value.
Q: Does it matter which point is (x1, y1) and which is (x2, y2)?
A: No, the formula will yield the same result as long as you are consistent.