# Translations

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Point Q is the image of point P under a dilation with center O and scale factor 4. If PQ = 18, then what is OP?

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all distances also scale by a factor of 4.

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Sorry, but that's not right :(
I really need to do this. Any help?

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what do you mean by "that's not right?" What calculation did you do?

Without loss of generality, we can take the distances to be measured along the x-axis.

We have two points, P and Q on the x-axis, where

OQ = 4(OP) because of the dilation.
Since PQ=18, that means that 3/4 of the distance OQ = 18.

So, OQ = 24 and OP = 6.

All because the distances grew by a factor of 4, as I said.

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Like I said, the answer is wrong! I put it into my online class and it said it was 6. Thanks a whole bunch, Steve.

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