Coordinate Geometry Flashcards

Grade 10 · Math · Flashcards

Essential formulas and concepts for coordinate geometry on the Cartesian plane.

Flashcards

Distance Formula: d = √[(x₂−x₁)²+(y₂−y₁)²] — derived from the Pythagorean theorem.
Midpoint Formula: M = ((x₁+x₂)/2, (y₁+y₂)/2)
Slope of a Line: m = (y₂−y₁)/(x₂−x₁); positive slope rises left to right, negative slope falls.
Slope-Intercept Form: y = mx + b, where m is slope and b is the y-intercept.
Point-Slope Form: y − y₁ = m(x − x₁), useful when you know one point and the slope.
Standard Form of a Line: ax + by + c = 0 or ax + by = c, where a, b, c are integers.
Parallel Lines: Same slope, different y-intercepts: m₁ = m₂, b₁ ≠ b₂.
Perpendicular Lines: Slopes are negative reciprocals: m₁ × m₂ = −1.
Circle Standard Form: (x−h)²+(y−k)²=r², centre (h,k) radius r.
Circle General Form: x²+y²+Dx+Ey+F=0; use completing the square to find centre and radius.
Point-to-Line Distance: From (x₀,y₀) to ax+by+c=0: d = |ax₀+by₀+c|/√(a²+b²).
Collinear Condition: Points A, B, C are collinear if slope AB = slope BC (or the area of triangle ABC = 0).
Section Formula: Point dividing segment (x₁,y₁)−(x₂,y₂) in ratio m:n is ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)).