Edexcel A Level Maths: Pure:復習筆記3.2.3 Bisection of Chords
Bisection of Chords
How can I find the equation of a perpendicular bisector?
- The?perpendicular bisector?of a line segment:
- is perpendicular to the line segment
- goes through the midpoint of the line segment
- ?The midpoint and gradient of the line segment between points?(x1,?y1)?and?(x2,?y2)?are given by the formulae
- ?The gradient of the perpendicular bisector is therefore
- The equation of the perpendicular bisector is the equation of the line with that gradient through the line segment's midpoint (see Equation of a Straight Line)
How can I use perpendicular bisectors to find the equation of a circle?
- A?chord?of a circle is a straight line segment between any two points on the circle
- The perpendicular bisector of a chord always goes through the centre of the circle
- If you know three points on a circle, draw two chords between them – the perpendicular bisectors of the chords will meet at the centre of the circle
- Now that you know the centre of the circle and a point on the circle you can write the equation of the circle
Exam Tip
- To find the point of intersection of two straight lines, set the equations of the lines equal to each other and solve.?
Worked Example
轉載自savemyexams
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