Let us see the alternative method to divide a line segment in a given ratio.
Draw a line segment of length \(6.2 \ cm\) and divide it in the ratio \(4:3\). Measure the two parts.
Step 1: Draw a line segment \(AB\) of length \(6.2 \ cm\).
Step 2: Draw any ray \(AX\), making an acute angle with \(AB\).
Step 3: Mark \(4\) points \(A_1\), \(A_2\), \(A_3\) and \(A_4\) on \(AX\) such that \(AA_1\) \(= A_1A_2\) \(= A_2A_3\) \(= A_3A_4\).
Step 4: Draw another ray \(BY\) parallel to \(AX\) and mark \(3\) points on \(BY\) such that \(BB_1\) \(= B_1B_2\) \(= B_2B_3\).
Step 5: Join \(A_4\) to \(B_3\). Let it intersect at \(C\) on \(AB\). Thus, \(AC: CB = 4:3\)
In \(\Delta AA_4C\) and \(\Delta BB_3C\):
\(CAA_4 = CBB_3\) (Since \(AX || BY\), the alternate interior angles are equal)
\(ACA_4 = BCC_3\) (Vertically opposite angles are equal)
Therefore, \(\Delta AA_4C \sim \Delta BB_3C\) (by AA similarity)
If two triangles are similar then their corresponding sides are in the same ratio.
By construction, we have:
Therefore, \(AC : BC = 4: 3\).