Question

To divide a line segment PQ in the ratio a : b (a, b are positive integers), draw a ray PX so that ∠QPX is an acute angle and then mark points on ray PX at equal distances such that minimum number of these points is

Answer 1

Given : divide a line segment PQ in the ratio a : b (a, b are positive integers), draw a ray PX so that ∠QPX is an acute angle and then mark points on ray PX at equal distances

To Find :  minimum number of these points is

(1) Greater ofa and b

(2) a+b

(3) a+b–1

(4) a+b+1

Solution:

To divide a line segment PQ  in the ratio a:b,

Step1 : Draw a line segment PQ  of some length

Step 2 :  Draw a Ray PX such that ∠QPX is an acute angle

Step 3:  Take a+b point on PX of Equal length one by one ( consecutively)

Step 4 :  Join a+b th Point with Q as a straight line

Step 5 : Draw a line parallel to line drawn in step 4 such that it passes through ath point of step 3 and intersect PQ at M

M divides PQ in to  a : b Ratio.

a+b points are required  

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