Coordinate geometry

• The formula for the gradient of a straight line from two points: (x1, y1) and (x2, y2) is m = (y2 - y1)/(x2 - x1).
• The equation of a straight line from a point (x', y') and gradient m is y - y' = m (x - x').
• Parallel lines have the same gradient.
• Perpendicular lines are normal to each other and so the gradient of a perpendicular line is -1/the gradient of the other line.
• The distance between two points (x1, y1) and (x2, y2) is d = root((x2 - x1)^2 + (y2 - y1)^2).
• The midpoint of a line segment with end points (x1, y1) and (x2, y2) is ((x1 + x2)/2 , (y1 +y2)/2).
• The equation of a circle with centre (a, b) and radius r is (x - a)^2 + (y - b)^2 = r^2.
• To find an intersection of two lines, equate their equations.
• The tangent to a circle is perpendicular to the radius of the circle at the point of intersection.
• The perpendicular bisector to a chord of a circle will pass through the centre of the circle.
• A circle that passes through all the vertices is called a circumcircle of the triangle. Each side of the triangle is a chord.
• If the triangle in a circumcircle is right angles, the hypotenuse will be the diameter of the circle.
• The centre of a circle can be found by finding the points of intersection of the perpendicular bisector of any two chords of the circle.
• Parametric equations define the x and y coordinates separately using a third variable, t.
• The domain of a cartesian function is the range of the parametric function for the x axis, and the range of the cartesian function is the range of the parametric function for the y axis.
• To find the point of intersection of a parametrically defined function and a cartesian function, convert the parametric function to a cartesian function by equating the t variables.