8.5 Chapter summary
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8.4 Mid-point of a line
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8.5 Chapter summary (EMA6J)
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A point is an ordered pair of numbers written as \(\left(x;y\right)\).
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Distance is a measure of the length between two points.
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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.
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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.
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The standard form of the straight line equation is \(y=mx+c\).
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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.
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If two lines are perpendicular, the product of their gradients is equal to \(-\text{1}\).
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For horizontal lines the gradient is equal to \(\text{0}\).
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For vertical lines the gradient is undefined.
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The formula for finding the mid-point between two points is:
\[M\left(x;y\right) = \left(\frac{{x}_{1} + {x}_{2}}{2};\frac{{y}_{1} + {y}_{2}}{2}\right)\]
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