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04 - Section Formula (explanation) - Class 10 - Maths Video Lecture
FAQs on 04 - Section Formula (explanation) - Class 10 - Maths Video Lecture
| 1. What is the section formula in mathematics? |  |
The section formula is a mathematical formula used to find the coordinates of a point that divides a line segment into a given ratio. It is used to find the coordinates of a point P(x, y) that lies on the line segment joining two given points A(x₁, y₁) and B(x₂, y₂), dividing it in the ratio m₁: m₂.
| 2. How can we apply the section formula to find the mid-point of a line segment? | |
To find the mid-point of a line segment using the section formula, we can use the ratio 1:1. Let's say we have two points A(x₁, y₁) and B(x₂, y₂). The mid-point M(x, y) can be found using the formula:
x = (x₁ + x₂) / 2 and y = (y₁ + y₂) / 2
This formula gives us the average of the x-coordinates and y-coordinates of the two given points, which gives us the mid-point.
| 3. How do we find the coordinates of a point that divides a line segment in a given ratio other than 1:1? | |
To find the coordinates of a point that divides a line segment in a given ratio other than 1:1, we can use the section formula. Let's say we have two points A(x₁, y₁) and B(x₂, y₂), and we want to divide the line segment in the ratio m₁: m₂. The coordinates of the point P(x, y) can be found using the formula:
x = ((m₁ * x₂) + (m₂ * x₁)) / (m₁ + m₂) and y = ((m₁ * y₂) + (m₂ * y₁)) / (m₁ + m₂)
By substituting the given values of m₁ and m₂, we can find the coordinates of the desired point.
| 4. Can the section formula be applied to find the coordinates of a point outside the line segment? | |
No, the section formula cannot be applied to find the coordinates of a point outside the line segment. The section formula is specifically used to find the coordinates of a point that lies on the line segment joining two given points. If the point lies outside the line segment, the section formula cannot be used to find its coordinates.
| 5. Is the section formula applicable only in two-dimensional space? | |
Yes, the section formula is applicable only in two-dimensional space. It is used to find the coordinates of a point on a line segment in a two-dimensional coordinate plane. In three-dimensional space, a different formula, known as the section formula in three dimensions, is used to find the coordinates of a point on a line segment.
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Dec 23, 2024 Last updated |
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