# 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 *\(l\)*.