The correct option is A Find the ratios in which the points P and Q divide line segment AB and then divide the line segment AB in the ratios obtained.
Given AP:PQ=1:2 and PQ:QB=4:5.
Dividing equation (1) by (2)
Hence Q divides AB in the ratio of 6:5.
Adding equations (1) and (2),
Dividing APPQ=12 by equation (4), we get
⇒ P divides line segment AB in the ratio of 2 : 9.
Now proceed further by dividing
line segment AB by the two ratios
respectively and thereby identifying