Edexcel Pure Maths Chapter 6|2023 LATEST UPDATEGUARANTEED SUCCCESS

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 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