Constructions & Loci (Edexcel IGCSE Maths B): Flashcards

A perpendicular bisector is a line that cuts another line exactly in half (bisects) and also crosses it at a right angle (perpendicular).

To construct a perpendicular bisector:

1. Set the distance between the point of the compasses and the pencil to be more than half the length of the line.

2. Place the point of the compasses on one end of the line and sketch an arc above and below the line.

3. Keeping your compasses set to the same distance, move the point of the compasses to the other end of the line and sketch an arc above and below it again.

4. The arcs should intersect each other both above and below the line, connect the points where the arcs intersect using a ruler.

True.

The shortest distance from a point to a line is a straight line, which meets the line at 90 degrees.

E.g. When finding the shortest distance between a boat and a coastline, construct a perpendicular line from the boat to the coastline.

To construct a perpendicular to a line, from a point:

1. Set the distance between the point of your compasses and the pencil to be greater than the distance between the point and the line.

2. Place the point of the compasses onto the point and draw an arc that intersects the line in two places.

3. Make sure that the distance between the point of the compasses and the pencil is greater than half the distance between the intersection points. Place the point of the compasses on a point of intersection, and sketch an arc above and below the line.

4. Keeping the distance between the point on the compasses and the pencil the same, do this again from the other point of intersection. These should intersect with the previous arcs.

5. Join the original point with the point where the arcs intersect.

An angle bisector is a line that cuts an angle exactly in half (bisect).

To construct an angle bisector:

1. Place the point of the compasses at the point of the angle and sketch an arc that intersects both of the lines that form the angle.

2. Set the distance between the point of your compasses and the pencil to be greater than half the distance between the intersection points. Place the point of the compasses on one of the points of intersection and sketch an arc.

3. Keeping the distance between the point of the compasses and the pencil the same, place the point of the compasses on the other point of intersection and sketch another arc, this should intersect the arc sketched in step 2.

4. Join the point of the angle to the point of intersection of the arcs with a ruler.