LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

CONSTRUCTION OF PERPENDICULAR TO A LINE FROM A POINT OUTSIDE THE LINE

__CONSTRUCTION OF PERPENDICULAR TO A LINE FROM A POINT OUTSIDE THE LINE -__

**Constructing a perpendicular line to a given line from a point outside the line involves several steps. Here's how you can do it using a compass and a straightedge:**

**Let's say you have a line ℓℓ and a point P outside that line, and you want to construct a line perpendicular to ℓℓ passing through point P.**

**Draw the given line ℓℓ and mark the point P outside it.**__Place the compass on point P:-__Put the compass needle on point P.__Adjust the compass width:-__Adjust the compass width to a length longer than the distance from point P to the line ℓℓ.__Draw an arc:-__With the compass set at the adjusted width, draw an arc that intersects the line ℓℓ at two points. Label these points of intersection as A and B.__Place the compass on A and B:-__Without changing the compass width, place**the compass needle on points A and B successively.**__Draw arcs:-__With the compass set at the same width, draw arcs with centers at points A and B such that they intersect above and below point P. Label these points of intersection as C and D.__Connect P with C and D:-__Use a straightedge to draw lines from point P to points C and D.__Draw the perpendicular line:-__The line PC or PD is the perpendicular line to ℓℓ passing through point P.

**The rationale behind this construction is that the perpendicular distance from the given line ℓℓ to point P is the shortest distance. By using arcs to find equidistant points on the line, we ensure that the lines PC and PD are perpendicular to ℓℓ.**

__Another Way Of Understanding:-__

**To draw a perpendicular to a line from a point outside the line.**

__Given:-__ A line AB and a point P outside AB.

__Required:-__ To draw a perpendicular to AB from the point P.

__Steps Of Construction:-__

__Step.1__) With P as centre and any suitable radius, draw an arc to cut the line AB at points C & D.

__Step.2__) With C & D as centres, draw two arcs of equal radius (>1/2 CD) cutting each other at Q on the other side of AB.

__Step.3__) Draw a line through P & Q to intersect the line AB at N, then segment PN is the required perpendicular from the point P to the line AB.