Q1
The mid-point formula is a special case of the section formula for ratio:
A1:1
B2:1
C1:2
D3:1
CBSEClass 10 (CBSE)MathematicsCh 7 · Topic 2
Section Formula
Learning to find the coordinates of a point dividing a line segment in a given ratio.
Core concept
A special and very commonly used case of the section formula occurs when the ratio is 1:1, which simplifies to the mid-point formula: [(x₁+x₂)/2, (y₁+y₂)/2] — the average of the x-coordinates and the average of the y-coordinates. The section formula has practical applications in geometry, such as finding centroids of triangles (which divide medians in a 2:1 ratio) and in fields like computer graphics for smoothly interpolating between two points.
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• Section formula finds a point dividing a segment in ratio m:n: [(mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)].
• The mid-point formula is a special case for ratio 1:1: [(x₁+x₂)/2, (y₁+y₂)/2].
• Section formula is used to find triangle centroids (dividing medians in 2:1 ratio).
• Also used in computer graphics for interpolating between two points.