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8.5 Chapter summary (EMA6J)

Presentation: 2GDQ

  • A point is an ordered pair of numbers written as \(\left(x;y\right)\).

  • Distance is a measure of the length between two points.

  • The formula for finding the distance between any two points is:

    \[d = \sqrt{{\left({x}_{1} - {x}_{2}\right)}^{2} + {\left({y}_{1} - {y}_{2}\right)}^{2}}\]
  • The gradient between two points is determined by the ratio of vertical change to horizontal change.

  • The formula for finding the gradient of a line is:

    \[m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}\]
  • A straight line is a set of points with a constant gradient between any two of the points.

  • The standard form of the straight line equation is \(y=mx+c\).

  • The equation of a straight line can also be written as

    \[\frac{y - {y}_{1}}{x - {x}_{1}} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}\]
  • If two lines are parallel, their gradients are equal.

  • If two lines are perpendicular, the product of their gradients is equal to \(-\text{1}\).

  • For horizontal lines the gradient is equal to \(\text{0}\).

  • For vertical lines the gradient is undefined.

  • The formula for finding the mid-point between two points is:

    \[M\left(x;y\right) = \left(\frac{{x}_{1} + {x}_{2}}{2};\frac{{y}_{1} + {y}_{2}}{2}\right)\]