Ex.10.1 Q2 Practical Geometry Solution - NCERT Maths Class 7
Question
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 –
- Draw a line \( l\), take a point \(P\) on it. Draw a perpendicular passing trough point \(P.\)
- 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 \(Y\).
- Taking \(Y\) as centre and with a convenient radius, draw an arc intersecting \(l\) at \(A\) and \(XY\) at \(B\).
- 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 \(AB\).
- Without changing the opening of compass and taking \(E\) as the centre, draw an arc to intersect the previously drawn arc \(CD\) at \(F\).
- Join the points \(X\) and\( F\) to draw a line \(\rm m.\)
Line \(\rm m\) is the required line which is parallel to \(l\).