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The Distance Formula 𝑑 = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2 Used to find the length of a line The Midpoint Formula x1 x2 y1 y2 M , 2 2 Used to determine if line segments bisect each other Find the center of a circle The Slope Formula m y 2 y1 x 2 x1 Used to determine if lines are parallel (same slope) Used to determine if lines are perpendicular (negative reciprocal slopes) Slope-Intercept Form of the Equation of a Line y mx b slope y-intercept Point-Slope Form of the Equation of a Line Point-Slope Form of the Equation of a Line: y y1 m x x1 m = slope The Equation of a Circle: x h h, k = 2 y k r2 center 2 r = radius (x1,y1) = a point on the line Common Core Geometry Formulas to Remember Altitude Rule The altitude is the mean proportional between the measures of the segments of the hypotenuse Leg Rule Each leg of a right triangle is the mean proportional between the whole hypotenuse and the projection of the leg on the hypotenuse. H L L S S A A S Trigonometry The three trigonometric ratios compare these sides from the point of view of one of the acute angles (not the right angle) in a right triangle: Use this phrase to memorize the three trigonometric ratios: 𝒔𝒊𝒏 (𝒂𝒄𝒖𝒕𝒆 ∡) = 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 𝒄𝒐𝒔 (𝒂𝒄𝒖𝒕𝒆 ∡) = 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 𝒕𝒂𝒏 (𝒂𝒄𝒖𝒕𝒆 ∡) = 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 SOH CAH TOA Convert Degrees to Radians (vice versa) To convert from degrees to radians MULTIPLY BY To convert from radians to degrees Arc Length Formula Formula: s r MULTIPLY BY 𝜋 180 180 𝜋 Area of a Sector Formula Formula: A 1 2 r 2