Draw a line perpendicular to a line segment AB measuring 4.7 cm from a point not lying on it.
Answers
Answer:
Steps of Construction :
1. With P and Q as centers, draw arcs on both sides of PQ with equal radii. The radius should be more than half the length of PQ.
2. Let these arcs cut each other at points R and RS
3. Join RS which cuts PQ at D. Then RS=PQ. Also ∠POR=90
∘
.
Hence, the line segment RS is the perpendicular bisector of PQ as it bisects PQ at P and is also perpendicular to PQ. On measuring the lengths of PR=4cm, QR=4 cm Since PR=QR, both are 4cm each
∴PR=QR.
Answer:
Objective
This topic gives an overview of;
Line Segment
Construction of a line segment of a given length
Constructing a copy of a given Line Segment.
Perpendicular to a line through a point on it
Perpendicular bisector of a line segment
A Line Segment
Remember that a line segment is bounded by two end-points. This makes it possible to measure its length with a ruler. If we know the length of a line segment, it becomes possible to represent it by a diagram. Let us see how we do this.
Construction of a line segment of a given length
Suppose we want to draw a line segment of length 4.7 cm. We can use our ruler and mark two points A and B which are 4.7 cm apart. Join A and B and get AB. While marking the points A and B, we should look straight down at the measuring device. Otherwise we will get an incorrect value.
Use of ruler and compasses
A better method would be to use compasses to construct a line segment of a given length.
Step 1: Draw a line l. Mark a point A on a line l.

Step 2: Place the compasses pointer on the zero mark of the ruler. Open it to place the pencil point upto the 4.7cm mark.

Step 3: Taking caution that the opening of the compasses has not changed, place the pointer on A and swing an arc to cut l at B.

Step 4: AB is a line segment of required length.

Constructing a copy of a given Line Segment.l
Suppose you want to draw a line segment whose length is equal to that of a given line segment AB.
A quick and natural approach is to use your ruler (which is marked with centimetres and millimetres) to measure the length of AB and then use the same length to draw another line segment CD
A second approach would be to use a transparent sheet and trace AB onto another portion of the paper. But these methods er-compasses” construction as follows:
Step 1: Given a point P on a line l. 
Step 2: With P as centre and a convenient radius, construct an arc intersecting the line l at two points A and B.

Step 3: With A and B as centres and a radius greater than AP construct two arcs, which cut each other at Q.

Step 4: Join PQ. Then  is perpendicular to l. We write  ⊥ l.
Perpendicular to a line through a point not on it
If we are given a line l and a point P not lying on it and we want to draw a perpendicular to l through P, we can again do it by a simple paper folding as before. Take a sheet of paper (preferably transparent). Draw any line l on it. Mark a point P away from l. Fold the sheet such that the crease passes through P. The parts of the line l on both sides of the fold should overlap each 0
The perpendicular bisector of a line segment

Fold a sheet of paper. Let AB be the fold. Place an ink-dot X, anywhere. Find the image X' of X, with AB as the mirror line.
Let AB and XX’ intersect at O. OX = OX'. This means that AB divides XX’ into two parts of equal length. AB bisects XX’ or AB is a bisector of XX’. Note also that ∠AOX and ∠BOX are right angles. Hence, AB is the perpendicular bisector of XX’. We see only a part of AB in the figure. The perpendicular bisector of a line joining two points is
same as the axis of symmetry
Step 1: Draw a line segment AB.
Step 2: Place a strip of a transparent rectangular tape diagonally across AB with the edges of the tape on the end points A and B, as shown in the figure.
Step 3: Repeat the process by placing another tape over A and B just diagonally across the previous one. The two strips cross at M and N.
Step 4: Join M and N.
Summary
Two lines are said to be perpendicular when they intersect each other at an angle of 90o.