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.
3 lessons, about 1 h 30 min3 simulations11 problems7 practice questionsPython in every lesson
Created by StemPy LabA locus is the path of a point that obeys a rule. To find its equation, call the moving point , write the rule in and , and simplify. Equal distances from two points give a line, and a right angle at gives a circle.
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.
The centroid is the average of the corners. The orthocentre is where the altitudes meet, and the circumcentre is where the perpendicular bisectors meet. These three lie on one line, with . The incentre is the average weighted by the opposite sides. A pair of lines through the origin has the equation .
Log in to join the discussion.
Loading…