coordinate geometry
(chapter 7)
click to edit
How to find midpoint?
Use midpoint formula: ↓
Parallel & perpendicular lines, collinear points
How to find length of line segment?
Use length of line segment formula: ↓
TB pg 143 worked example 3 part(ii):
TB pg 143 worked example 3 part(i):
If all points lie on the same line → collinear points
Parallel lines
Perpendicular lines
If two lines are parallel to each other → their gradients are equal
notation // to denote 'is parallel to'
e.g: AB//CD → AB is parallel to CD
- If two lines are perpendicular to each other → their gradient is negative reciprocal (-1)
- The gradient of product of two perpendicular lines is -1
notation ⊥ to denote 'is perpendicular to'
e.g: AB⊥CD → AB is perpendicular to CD
TB pg 153 worked example 9
part (i) and (ii):
Area of polygon (shoelace method)
example:
Note!! :
- vertex must be written in an anticlockwise direction
- repeat the 1st coordinate
Circles
Equation of straight line
y = mx + c
Perpendicular bisector
(expanded from perpendicular lines)
steps:
- find midpoint
- find ⊥ gradient
example:
equation of circle
general equation →
not told about radius or centre
from standard equation to general equation [expand!!]
Ratio Theorem
Note!!
- cuts the y-axis: x = 0
- cuts the x-axis: y = 0
complete the square (converting general to standard equation
use midpoint to find missing vertex:
- square
- rectangle
- rhombus
- parallelogram
standard equation → given radius
and coordinates of centre
To find radius and centre coordinates:
To find radius and centre coordinates:
example1 : worked example16
position of point/chord
key words
outside:
inside:
on: the distance of centre to the point will equal to the radius
Example:
sketching graph of completing the square
Note!!
- find the equation of line -> point and gradient
- find the equation of circle -> radius and centre
Finding equation of circle, given two points and a line (refer to Tb pg 168 worked example 17)
- find midpoint and gradient of the two points
- using midpoint & gradient, form an equation of perpendicular bisector
- do simultaneous equation with the equation of perpendicular bisector and the line to find the centre of circle
- using the centre of circle, find the radius of circle
- use the centre and radius to form the equation of circle