FORMULAS/EQUATIONS Distance Formula If ( ) = P x y , 1 1 1 and ( ) = P x y , , 2 2 2 the distance from P1 to P2 is ( ) ( ) ( ) = − + − d P P x x y y , 1 2 2 1 2 2 1 2 Standard Equation of a Circle The standard equation of a circle of radius r with center at ( ) h k , is ( ) ( ) − + − = x h y k r 2 2 2 Slope Formula The slope m of the line containing the points ( ) = P x y , 1 1 1 and ( ) = P x y , 2 2 2 is = − − ≠ = m y y x x x x m x x if is undefined if 2 1 2 1 1 2 1 2 Point–Slope Equation of a Line The equation of a line with slope m containing the point ( ) x y , 1 1 is ( ) − = − y y m x x 1 1 Slope–Intercept Equation of a Line The equation of a line with slope m and y-intercept b is = + y mx b Quadratic Formula The solutions of the equation + + = ≠ ax bx c a 0, 0, 2 are = − ± − x b b ac a 4 2 2 If − > b ac 4 0, 2 there are two unequal real solutions. If − = b ac 4 0, 2 there is a repeated real solution. If − < b ac 4 0, 2 there are two complex solutions that are not real. GEOMETRY FORMULAS Circle r = = = r A C Radius, Area, Circumference π π = = A r C r 2 2 Triangle h b = = b h Base, Altitude (Height), = A area = A bh 1 2 Rectangle l w = = = = l w A P Length, Width, area, perimeter = = + A lw P l w 2 2 Rectangular Box (closed) h w l = = = = = l w h V S Length, Width, Height, Volume, Surface area = = + + VlwhS lw lh wh 2 2 2 Sphere r = = = r V S Radius, Volume, Surface area π π = = V r S r 4 4 3 3 2 Right Circular Cylinder (closed) h r = = = = r h V S Radius, Height, Volume, Surface area π π π = = + V r h S r rh 2 2 2 2
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