How to find a midpoint of a line segment
Average the x and y coordinates of its end points; (x1+x2/2),(y1+y2/2)
What's a line segment
A finite
... [Show More] part of a straight line with two distinctive end points
What's it helpful to do in coordinate geometry?
Draw a sketch showing the info given in the question
What's the perpendicular bisector of line AB?
The straight line perpendicular to AB and that also passes through its midpoint
What is a circle?
A set of points that are equidistant from a set point. You can use Pythagoras to derive equations of circles on a coordinate grid. For any point (x,y) of the circumference of a circle, you can use Pythagoras to show the relationship between x, y and r
What's the equation of a circle with centre (0,0) and radius r?
x^2+y^2=r^2
What's the equation of a circle with centre (a,b) and radius r?
(x-a)^2 + (y-b)^2 = r^2 (this is the translation of the circle x^2+y^2=r^2 by the vector ai+bj)
What's the safest way to find the centre and radius of a circle with an equation given in expanded form?
Complete the square for the x and y terms
How many times can a straight line intersect a circle?
0,1 or 2
What is a tangent to a circle?
A straight line that intersects the circle at only one point, and is perpendicular to the radius of the circle at the point of intersection
What is a chord?
A line segment joining 2 points on a circles circumference (the diameter of the circle is also the longest chord). The perpendicular bisector or a chord will go through the centre of the circle
If a gradient is given as a fraction, how can you find the perpendicular gradient?
Turning the fraction upside down and changing the sign
How can you find the point(s) of intersection for a straight line and circle?
Using the discriminant
What is a circumcircle?
Where you draw a unique circle round the three vertices of any triangle
What is a circumcentre?
The centre of the circle is called the circumcentre of the triangle and is the point where the perpendicular bisectors of each side interact
What are other ways of stating that for a right angled triangle, the hypotenuse of the triangle is the diameter of the circumcircle?
-if PQR=90° then R lies on the circle with diameter PQ
-the angle in a semicircle is always a right angle [Show Less]