Question

Draw a line segment PQ = 6.5 cm. Take any point M outside it. Using a ruler and compass, draw a line through M parallel to PQ.

Answer 1

Hint: First of all, draw a line PQ and any point M outside it and join M to any point on line PQ and name it M. Now, to make a line parallel to PQ, we will find point W and join it to M to get MQ as a parallel line. For this, we will draw arc M and N as the centre and accordingly we will find the new point W.

Complete step-by-step answer:
In this question, first, we have to draw a line segment PQ = 6.5 cm. Now, we have to take point M outside it and using a ruler and compass, we have to draw a line through M parallel to PQ. Let us see the steps to carry out the above process.
1. First of all, let us draw a line segment of length 6.5 cm using the ruler and name its ends P and Q.

2. Let us take a point M out this line

3. Now, let us take any point N on the line segment PQ and join the point M to N as follows.

4. Now, with N as centre and radius less than MN, draw an arc cutting NQ at x and NM as y as follows by using compass.

5. Now, with the same radius as in the previous step and with centre M, draw an arc AB cutting MN at z as follows.

6. Now, take the radius equal to xy and with the centre as z, draw an arc cutting AB at w as follows.

7. Now, join M to w and extend it to both sides as follows.

8. Hence, the new line l is parallel to line PQ.

Note: Students must note that the distance between two parallel lines is always constant. So, they can verify their construction by finding the distance between the two lines at different points using the ruler and checking if it is the same at all points or not. Note that the distance should be the perpendicular distance between both the lines. Also, students must remember that to draw a line, we need at least two points and that’s why we have found point w along with M.