Straight line graphs
The distance between two points can be calculated by constructing a right-angled triangle between the coordinates and applying Pythagoras’ Theorem:
The coordinate of the midpoint of the line between the points (????1, ????1) and (????2, ????2) is given by:
If C divides the line AB in the ratio p : q where A(????1, ????1) and B(????2, ????2):
The gradient of the line between the points (????1, ????1) and (????2, ????2) is given by:
Given the gradient, ????, and a single point, (????1, ????1), the equation of a line can be generated using:
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If the lines with the gradients m1 and m2 are parallel:
The perpendicular bisector of the line AB is a straight line that is
- Perpendicular to line AB
- Passes through the midpoint of line AB
If the gradient of AB is m then the gradient of its perpendicular bisector is:
Equation of circle
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The tangent to the circle is perpendicular to the radius of the circle at the intersection point.
The perpendicular bisector to a chord of the circle will pass through the centre C.