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Draw a Line Segment Ab of Length 7 Cm. Using Ruler and Compasses, Find a Point P on Ab Such that a P a B = 3 5 . - CBSE Class 10 - Mathematics

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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

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`.

  Is there an error in this question or solution?
Solution Draw a Line Segment Ab of Length 7 Cm. Using Ruler and Compasses, Find a Point P on Ab Such that a P a B = 3 5 . Concept: Division of a Line Segment.
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