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coordinate geometry (chapter 7) - Coggle Diagram
coordinate geometry
(chapter 7)
How to find midpoint?
Use midpoint formula: ↓
use midpoint to find missing vertex:
square
rectangle
rhombus
parallelogram
TB pg 143 worked example 3 part(i):
Parallel & perpendicular lines, collinear points
If all points lie on the same line →
collinear
points
Parallel 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
Perpendicular lines
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):
How to find length of line segment?
Use length of line segment formula: ↓
TB pg 143 worked example 3 part(ii):
Equation of straight line
y = mx + c
Area of polygon (shoelace method)
example:
Note!!
:
vertex must be written in an anticlockwise direction
repeat the 1st coordinate
Circles
equation of circle
general equation →
not told about radius or centre
To find radius and centre coordinates:
from standard equation to general equation [expand!!]
standard equation → given radius
and coordinates of centre
To find radius and centre coordinates:
complete the square (converting general to standard equation
example1 : worked example16
sketching graph of completing the square
position of point/chord
outside:
inside:
on: the distance of centre to the point will equal to the radius
Example:
key words
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
Perpendicular bisector
(expanded from perpendicular lines)
steps:
find midpoint
find ⊥ gradient
example:
Note!!
cuts the y-axis: x = 0
cuts the x-axis: y = 0
Ratio Theorem
