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# Summary

## 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; $$m = \tan \theta$$