Variables are not constants!

Geometry Level 2

The line joining points ( 2 m + 2 , 2 m ) (2m + 2,2m) & ( 2 m + 1 , 3 ) (2m+1,3) passes through ( m + 1 , 1 ) (m +1,1) .

What is the product of all possible values of m m ?


The answer is -1.

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1 solution

Reljod Oreta
Aug 16, 2014

They are in one line so there slopes are equal..

m1 of (2m+2,2m) and (2m+1,3) is equal to m2 of (2m+2,2m) and (m+1,1)

m=(y2-y1)/(x2-x1)

m1= (2m-3)

m2= (2m-1)/(m+1)

m1=m2 so (2m-3)=(2m-1)/(m+1) then get m

so m= -1/2 and 2

-1/2*2= -1

An elegant & complete solution!!!!!!

Harsh Shrivastava - 6 years, 10 months ago

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