How can we divide any line segment in a given ratio?
21 Jan 2015, 11:35 PM
1. Draw any ray OP, making an acute angle with OQ.
2. Locate 5 = (m + n) points O1,O2,O3,O4 and O5 on OP so that OO1 = O1O2 = O2O3 =O3O4 = O4O5.
3. Join QO5
4. Through the point O3(m = 3), draw a line parallel to O5Q (by making an angle equal to LOO5Q) at O3 intersecting OQ at point R then, OR: RQ = 3:2.
Let us see how this method gives us the required division.
Since O3R is parallel to O5Q, therefore
OO3/O3O5 = OR/RQ....................... (By basic proportionality theorem)
By construction, OO3/O3O5 = 3/2.
This shows that R divides OQ in the ratio 3:2
Login to add comment 23 Jan 2015, 12:58 AM