Ch 7 applies algebra to geometry through formulas for distance, section division, and area. These formulas bridge algebra and geometry, enabling computational solutions to geometric problems.
Distance between points (x₁,y₁) and (x₂,y₂) = √[(x₂−x₁)² + (y₂−y₁)²]. Derived from Pythagoras theorem. Used to find lengths and verify shape properties.
Point dividing the line segment joining (x₁,y₁) and (x₂,y₂) in ratio m:n is ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)). Midpoint is the special case m = n = 1.
Area = ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|. If area = 0, the three points are collinear. This formula works for any triangle in the coordinate plane.
Download: https://ncert.nic.in/textbook/pdf/jemh107.pdf | Complete book: https://ncert.nic.in/textbook/pdf/jemh1ps.zip
Three points are collinear if they lie on the same straight line. Using the area formula: if the area of the triangle formed by three points is 0, they are collinear.
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