Ex.10.1 Q2 Practical Geometry Solution - NCERT Maths Class 7

Draw a line \(l\). Draw a perpendicular to \(l\) at any point on \(l\). On this perpendicular choose a point \(X\), \(4 \rm\, cm \) away from \(l\). Through \(X\), draw a line \(m\) parallel to \(l\).

Text Solution

What is known?

A line \(l\) and \(m\) which are \(4\,\rm{cm}\) apart.

To construct:

A perpendicular at any point on line \( l\), and then draw a line \(m\) parallel to \(l\) through \(X\) on the perpendicular which is \(4\) cm from the line \(l\).

Reasoning:

Draw a line \(l\) and then a perpendicular to \( l\) at any point on \( l\). On this perpendicular choose a point \(X\), \(4\) cm away from \(l\). Through \(X\), draw a line \(m\) parallel to \( l\). Follow the steps given below.

Steps:

Steps of construction –

1. Draw a line \( l\), take a point \(P\) on it. Draw a perpendicular passing trough point \(P.\)
2. Now adjust the compass up-to the length of \(4\) \(\rm cm.\) Draw an arc to intersect this perpendicular at point \(X\) choose any point \(Y\) on line \(l \), join \(X\) to \(Y\).
3. Taking \(Y\) as centre and with a convenient radius, draw an arc intersecting \(l\) at \(A\) and \(XY\) at \(B\).
4. Taking \(X\) as centre and with the same radius as above, draw an arc \(CD\) cutting \(XY\) at \(E\)Adjust the compass up-to to the length of \(AB\).
5. Without changing the opening of compass and taking \(E\) as the centre, draw an arc to intersect the previously drawn arc \(CD\) at \(F\).
6. Join the points \(X\) and\( F\) to draw a line \(\rm m.\)

Line \(\rm m\) is the required line which is parallel to \(l\).