Q1
What is the mid-point formula?
A((x₁+x₂)/2, (y₁+y₂)/2)
B(x₁+x₂, y₁+y₂)
C(x₁-x₂, y₁-y₂)
D(x₁×x₂, y₁×y₂)
ICSEClass 10 (ICSE)MathematicsCh 13 · Topic 1
Section and Mid-Point Formula
The section formula finds a point dividing a line segment in a given ratio, while the mid-point formula finds the exact middle point.
Core concept
The mid-point formula is ((x₁+x₂)/2, (y₁+y₂)/2), averaging the x and y coordinates of two endpoints.
How it works
The section formula for a point dividing a segment in ratio m:n is ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)).
Why it matters
These formulas are useful for finding specific points along a line segment, like the centroid of a triangle or dividing points for construction.
Key detail
Understanding these formulas is essential for coordinate geometry problems involving points, segments, and geometric properties.
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Quick notes
• Mid-point formula: ((x₁+x₂)/2, (y₁+y₂)/2).
• It averages x and y coordinates.
• Section formula (ratio m:n): ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)).
• These find points along a segment.
• Used for triangle centroids.
• Also used for construction dividing points.
• Essential for coordinate geometry problems.
• Practice builds formula application skills.