DISTANCE
Definition Of Distance
he Distance between two points is defined as the shortest length between them.
More About Distance
Distance is a scalar quantity.
Example Of Distance
The line joining the open and closed books is a vertical line.
The length of a vertical line-segment on a coordinate plane equals the difference between the y-coordinates.
So, the distance between the two books = 20 - 5 = 15 units.
Video Examples: Algebra - Distance Formula (not upside down)
Solved Example on Distance
Ques: Find the distance between the two points A and B.
Choices:
A. 6 units
B. 8 units
C. 4 units
D. 2 units
Correct Answer: A
Solution:
Step 1: The line joining the two points A and B is a horizontal line-segment.
Step 2: The length of a horizontal line-segment on a coordinate plane equals the difference between the x - coordinates.
Step 3: Point A is located at the ordered pair (2, 4) and point B is located at the ordered pair (8, 4).
Step 4: So, the distance between the two points A and B = 8 - 2 = 6. [Difference between the x - coordinates.]
Step 5: The distance between the two points A and B is 6 units.
Quick Summary
- Distance is a scalar quantity.
- Distance can be found using coordinate differences.
⚠️ Common Mistakes
- Confusing distance with displacement
- Incorrectly applying the distance formula
- Forgetting to take the square root
🌍 Real-World Uses
- Calculating the driving distance between two cities using GPS coordinates.
- Measuring the distance a baseball travels from the bat to where it lands.
- Determining the distance between two stars in astronomy using parallax and trigonometry.
📋 Standards Alignment
CCSS.MATH.CONTENT.8.G.B.7CCSS.MATH.CONTENT.HSG.GPE.B.7
🔗 Related Links
🍎 Teacher Insights
Use visual aids to demonstrate the concept of distance on a coordinate plane. Emphasize the connection between the distance formula and the Pythagorean theorem.🎓 Prerequisites
- Coordinate Plane
- Number Line
- Absolute Value
Check Your Knowledge
Q1: What is the distance between points (2, 4) and (8, 4)?
Q2: Which of the following is a scalar quantity?
Frequently Asked Questions
Q: Is distance always positive?
A: Yes, distance is a scalar quantity representing length, and length cannot be negative.
Q: How does the distance formula relate to the Pythagorean theorem?
A: The distance formula is derived from the Pythagorean theorem by considering the horizontal and vertical differences between two points as the legs of a right triangle.