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# if the lines y=mrx(r is subscript) r=1,2,3 cuts equsl intersepts on the transversal x+y=1then 1+m1,1+m2,1+me are in

Shukant Pal
25 Points
3 years ago
The equation of transversal x + y = 1 can also be written as x/1 + y/1 = 1. Therefore, it makes intercepts 1 on x and y axes. So, the (0,1) and (1,0) are coordinates of intersection with axes.

Now, three lines passing through the centre cut equal intercepts on the transveral or divide the portion (0,1) to (1,0) in 4 equal parts. By using the section formula you will get three points → (3/4, 1/4), (1/2, 1/2), and (1/4, 3/4). Clearly the lines passing through these 3 points and origin will have the slopes → 1/3, 1, and 3. Thus, mr, r=1,2,3 are in G.P. with common factor 3.