Untitled Flashcards Set

1. Distance Formula

d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

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2. Midpoint Formula

M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)

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3. Slope Formula

m = \frac{y_2 - y_1}{x_2 - x_1}

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4. Slope-Intercept Form

y = mx + b

• m: slope
  
  

• b: y-intercept
  
  

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5. Point-Slope Form

y - y_1 = m(x - x_1)

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6. Area of Triangle Using Trigonometry

A = \frac{1}{2}ab \sin(C)

• a, b: two sides
  
  

• C: included angle
  
  

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7. Area of a Sector

A = \frac{\theta}{360^\circ} \cdot \pi r^2

• \theta: central angle in degrees
  
  

• r: radius
  
  

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8. Partitioning a Line Segment (Scalar Form)

x = x_1 + k(x_2 - x_1)

y = y_1 + k(y_2 - y_1)

• k = \frac{m}{m + n}, where m:n is the ratio
  
  

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9. Density Formula

\text{Density} = \frac{\text{Mass}}{\text{Volume}}

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10. Equation of a Circle

(x - h)^2 + (y - k)^2 = r^2

• Center: (h, k)
  
  

• Radius: r