Class 10 Exam > Class 10 Videos > 02 - Distance Formula (explanation) - Class 10 - Maths
02 - Distance Formula (explanation) - Class 10 - Maths Video Lecture
FAQs on 02 - Distance Formula (explanation) - Class 10 - Maths Video Lecture
| 1. What is the distance formula? |  |
Ans. The distance formula is a mathematical equation used to calculate the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem and is given by the formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
| 2. How do you find the distance between two points using the distance formula? | |
Ans. To find the distance between two points using the distance formula, follow these steps:
1. Identify the coordinates of the two points, let's say (x1, y1) and (x2, y2).
2. Plug the values of x1, y1, x2, and y2 into the distance formula: Distance = √((x2 - x1)^2 + (y2 - y1)^2).
3. Simplify the formula by subtracting x2 from x1 and y2 from y1, and then square the differences.
4. Add the squared differences together and take the square root of the sum to find the distance between the two points.
| 3. How is the distance formula related to the Pythagorean theorem? | |
Ans. The distance formula is derived from the Pythagorean theorem. In a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Similarly, when we have two points in a coordinate plane, we can consider the horizontal and vertical differences between them as the two sides of a right-angled triangle. By applying the Pythagorean theorem to this triangle, we can derive the distance formula.
| 4. Can the distance formula be used in any coordinate system? | |
Ans. Yes, the distance formula can be used in any coordinate system, including two-dimensional (2D) and three-dimensional (3D) coordinate systems.
In a 2D coordinate system, the formula remains the same as mentioned earlier: Distance = √((x2 - x1)^2 + (y2 - y1)^2).
In a 3D coordinate system, an additional term is added to the formula to consider the difference in the z-coordinates of the two points: Distance = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2).
| 5. How is the distance formula used in real-life applications? | |
Ans. The distance formula has various real-life applications, including:
- Determining the distance between two cities on a map.
- Calculating the length of a diagonal in a rectangle or square.
- Finding the distance between two players in a sports field.
- Measuring the straight-line distance between two landmarks.
- Analyzing the proximity of objects in a coordinate plane, such as in GPS navigation systems.
These are just a few examples, but the distance formula is widely used in many fields where measuring distances between points is necessary.
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Dec 23, 2024 Last updated |
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