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Let J and K be given points along a certain line. There are exactly two other distinct points U and V on this line such that UJ/UK=7 and VJ/VK=7. Let W be the midpoint of UV. Calculate the ratio WJ/WK.

 Apr 24, 2021
 #1
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I think there might be an error in the question... that its \({VK \over VJ}=7\) in the second line pls note. 

Now, let's assume this is the line       

                                        ____•__________•_________•____

                                       J       V                   W                U       K

and, \({UJ \over UK}=7\)

⇒     \(UJ=7UK\)

 

       \({VK \over VJ}=7\)

⇒    \(VK = 7VJ\) 

 

Now, \(JK=VJ+VK\)                 And, \(JK= UJ+UK\)

                 \(=8VJ\)                                            \(=8UK\)

 

From this we infer that... \(VJ=UK\)

Also it is given that, W is midpoint of UV

\(VW=UW\)

 

∴ \({WJ \over WK} = {VW+VJ \over UW+UK}\)

            \(={VW+VJ \over VW+VJ}\)

            \(=1\)

 

The required ratio is 1. 

 Apr 24, 2021

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