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Summary

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4.6 Summary (EMBGH)

  • Distance between two points: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
  • Gradient of a line between two points: \(m = \dfrac{y_2 - y_1}{x_2 - x_1}\)
  • Mid-point of a line: \(M(x;y) = \left( \dfrac{x_1 + x_2}{2}; \dfrac{y_1 + y_2}{2} \right)\)
  • Parallel lines: \(m_1 = m_2\)
  • Perpendicular lines: \(m_1 \times m_2 = -1\)
  • General form of a straight line equation: \(ax + by + c = 0\)
  • Two-point form of a straight line equation: \(\dfrac{y - y_1}{x - x_1} = \dfrac{y_2 - y_1}{x_2 - x_1}\)
  • Gradient–point form of a straight line equation: \(y - y_1 = m(x - x_1)\)
  • Gradient–intercept form of a straight line equation (standard form): \(y = mx + c\)
  • Angle of inclination of a straight line: \(\theta\), the angle formed between the line and the positive \(x\)-axis; \(m = \tan \theta\)