Standard content

Beyond the textbook: the locus of a moving point, the bisectors of the angles between two lines, and the reflection of a point or ray in a line. Then the centres of a triangle and pairs of lines, the straight-line problems that JEE and A-Level Further Maths ask most, with a full timed paper.

What's inside

1. Locus of a point: A locus is the path of a point that obeys a rule. To find its equation, call the moving point $P(x, y)$, write the rule in $x$ and $y$, and simplify. Equal distances from two points give a line, and a right angle at $P$ gives a circle.
2. Angle bisectors and reflections: The points equally far from two lines lie on their two angle bisectors. Equate the two normalised expressions, once with a plus sign and once with a minus sign. With both constants positive, the plus sign gives the bisector of the angle that holds the origin. The image of a point in a mirror line goes as far beyond the line as the point is in front of it.