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# PLS HELP PLSSSS

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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

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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