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.

C

Steps of construction are:

1. Using a ruler, draw a line segment of length 7 cm.

2. If point P on AB divides AB such that AP : AB = 3:5,

then AP : PB = 3:2.

3. Using compass and ruler, draw a ray AX which makes

an acute angle PAX with AB.

4. Using compass and ruler, draw a ray BC which makes

an acute angle ABC with AB. X

5. Using a compass, mark three equal points on the line AX and

two points of the same length on BC.

6. Since P divides AB into a ratio 3:2, so join the third point of ray AX to the second point of BC.

7. The point where it cuts the line segment AB is the required point P which divides AB into a ratio 3:2 and also, AP: AB = 3:5 or .