8.5 Chapter summary

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:

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