Introduction to Construct a Perpendicular
Constructing a perpendicular means drawing a line at right angles to a given line from a given point. In case of curves, the perpendicular from a given point is to the tangent of the curve at the required point. Constructing perpendicular can be done in two ways. One method is by using a ruler and protractor and the other method is with the help of a compass and a ruler.
The second method is more accurate and let us study that.
Construct a Perpendicular – when the Point is on the Line
Look at the above diagram. To construct a perpendicular line l at point A in the line itself, the method is as follows.
1) Select two convenient points B and C on the line and on either side of A.
2) Set the compass for a radius of approximately more than half of the length BC.
3) Strike an arc from the point B..
4) Without changing the compass setting strike an arc from the point C..
5) Mark the point P where the arcs intersect.
6) Draw a line m passing through P and A.
Line m is the perpendicular to the line l.
Construct a Perpendicular – from a Point not on the Line
In this diagram, the point A is not on the line. To construct a perpendicular in this case, the steps are as follows.
1) With the help of the compass draw arcs from A to intersect the line at B and C.
2) Set the compass for a radius of approximately more than half of the length BC.
3) Strike an arc from the point B on the other side of the line.
4) Without changing the compass setting strike an arc on the same side from the point C..
5) Mark the point P where the arcs intersect.
6) Draw a line m passing through A and P.
Line m is the perpendicular to the line l. Understanding 30 60 90 Triangles is always challenging for me but thanks to all math help websites to help me out.
Construct a Perpendicular – Proof
You will observe that, in both the cases the line m connects the points of intersections of circles of same radius. As per theorems on circles, the line m bisects the line l, joining their centers at right angle.
Constructing a perpendicular means drawing a line at right angles to a given line from a given point. In case of curves, the perpendicular from a given point is to the tangent of the curve at the required point. Constructing perpendicular can be done in two ways. One method is by using a ruler and protractor and the other method is with the help of a compass and a ruler.
The second method is more accurate and let us study that.
Construct a Perpendicular – when the Point is on the Line
1) Select two convenient points B and C on the line and on either side of A.
2) Set the compass for a radius of approximately more than half of the length BC.
3) Strike an arc from the point B..
4) Without changing the compass setting strike an arc from the point C..
5) Mark the point P where the arcs intersect.
6) Draw a line m passing through P and A.
Line m is the perpendicular to the line l.
Construct a Perpendicular – from a Point not on the Line
In this diagram, the point A is not on the line. To construct a perpendicular in this case, the steps are as follows.
1) With the help of the compass draw arcs from A to intersect the line at B and C.
2) Set the compass for a radius of approximately more than half of the length BC.
3) Strike an arc from the point B on the other side of the line.
4) Without changing the compass setting strike an arc on the same side from the point C..
5) Mark the point P where the arcs intersect.
6) Draw a line m passing through A and P.
Line m is the perpendicular to the line l. Understanding 30 60 90 Triangles is always challenging for me but thanks to all math help websites to help me out.
Construct a Perpendicular – Proof
You will observe that, in both the cases the line m connects the points of intersections of circles of same radius. As per theorems on circles, the line m bisects the line l, joining their centers at right angle.
