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`.

 

 

Answer 1

It is given that`(AP)/(AB)=3/5`.

`therefore (AP)/(PB)=(AP)/(AB-AP)=3/(5-3)=3/2`

Thus, point P divides line segment AB in the ratio 3: 2. 

To draw a line segment AB of length 7 cm and mark a point P (using ruler and compass) such that `(AP)/(PB)=3/5 i,e, (AP)/(PB)=3/2`, the following steps are to be followed: 

Step 1: Draw line segment AB of length 7 cm and draw a ray AX making an acute angle with line segment AB. 

Step 2: Locate 5 (2 + 3) points i.e., A₁, A₂, A₃, A₄ and A₅ on AX such that AA₁ = A₁ A₂ = A₂ A₃ and so on. 

Step 3: Join BA₅.

Step 4: Through point A₃ , draw a line parallel to BA₅ (by making an angle equal to ∠AA₅ B) at A₃ intersecting AB at point P. 

Now, P is the required point on line segment AB of length 7 cm. This point satisfies the condition`(AP)/(AB)=3/5`.