Loci and Constructions Flashcards
What is a locus?
A path formed by a point which moves according to a rule.
What is a locus of points at equal distance around a point?
A circle.
Can areas be loci?
Yes, if a line moves.
What is the perpendicular distance between a point and a line?
The shortest distance.
How do find the perpendicular distance?
Firstly place the needle of a compass on the point and draw two arcs that the line. Then put the compass on the new points created where the arc goes through the line and and draw two arcs that connect to form another point. Then, connect this point with the original to find the perpendicular line.
How do you bisect a line?
Bisect means to split it into two equal pieces. Place the compass on each of the ending points in turn and draw two arcs. Then, join the two points where these arcs cross two bisect the line.
How do you bisect an angle?
You put the needle of the compass on the point where both lines intersect. You then draw an arc through both lines to form two points. Draw an arc from each of these points to form a third point. Then join this point with the first point.
How do you construct a triangle if you know the length of two of the sides and the angle in between?
You simply draw the angle with the sides around it, and join the ends of the sides together to form a triangle.
How do you construct a triangle if you know two angles and the side in between.
You draw one the angles off one side of the line and draw an extended line at that angle. Then draw the other angle, and where the two lines intersect are the top of the triangle.
How do you construct a triangle if you know the three sides?
You draw the first line. Then, around one point on the end of the line, you draw an arc with a compass with a radius of one of the sides. Then, do the other side at the other point. This forms a new point which is the top of the triangle.
What is a bearing?
A bearing shows the angle clockwise from north that a direction is
e.g. south = 180°
