6 - Coordinate Geometry Flashcards
gradient
chnage in y / change in x
= y -y1 / x-x1
equation of a straight line
y = mx + c
ax + by + c = 0
y - y1 = m(x- x1)
parallel/perpendicular lines
parallel - same gradient - m = m
perpendicular - negative reciprocal gradient - m = -1/m
distance between two point on a line
root ( chnage in x^2 + change in y ^2)
midpoint
(x+x1 /2), (y+y1 /2)
mathematical model
an attempt to model a real life situation based on mathematical concepts
properties of a perpendicular bisector of points A and B
- passes through midpoint of AB
- perpendicular to AB
equation of circle with centre 0,0
x^2 + y^2 = r^2
equation of circle with centre a,b
(x-a)^2 + (y-b)^2 = r^2
finding the intersection of two lines
solve simultaneously
can use discriminant to find no. intersections
a perpendicular bisector of any chord will always…
pass through the centre of the circle
a tangent is… to the radius
perpendicular
inscribes
a shape inscribes another if it’s inside it and it’s boundaries touch but do not intersect the outer shape
circumscribes
a shape inscribing a circle
the circle is know as the circumcircle of the other shape
the centre is known as the circumcenter
how to find the centre of a circumcircle
- if one angle (ABC) is 90 then the hypotenuse (AC) is the diameter - the centre is the midpoint of this (or vice versa if you are given that AC is the diameter
- find the equation of the perpendicular bisectors of the sides of the triangle - find the intersection of these lines
