Keep absolute positioned item in the same place regardless of the screen size

Hello,

I am working on waldo style app. When user finds a character i want to display a checkmark in that position. Currently, i am using offsetX and offsetY of the image to display checkmark. However the problem i am encoutering is that when you resize the screen checkmar's position gets all messed up because i am using fixed units. Is there a way to make sure that checkmark element always stays in the same position regardless of the screen size?
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