Chapter summary
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8.5 Chapter summary (EMA6J)

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 midpoint between two points is:
\[M\left(x;y\right) = \left(\frac{{x}_{1} + {x}_{2}}{2};\frac{{y}_{1} + {y}_{2}}{2}\right)\]
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