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.
+526 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.
