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Question
Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that `(AP)/(AB) = 3/5 `.
Solution
Steps of Construction:
Step 1: Draw a line segment AB = 7 cm
Step 2: Draw a ray AX, making an acute angle ∠BAX.
Step 3: Along AX, mark 5 points (greater of 3 and 5) `A^1 , A^2 , A^3 , A^4 and A^5` such that
`A A_1 = A_1 A_2 = A_ A_3 = A_3 A_4 = A_4 A_5`
Step 4: Join A5 B.
Step 5: From A3 , draw A3 P parallel to A5B ( draw an angle equal to 5 ∠AA5 B ), meeting AB in P.
`"Here, P is the point on AB such that"(AP)/(PB) =3/2 or (AP)/(AB) = 3/5.`
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