The right side of your brain processes and controls the left side of your body and senses, and the left does the same for the right.
If you have a stroke, or trauma, to the right side of your brain then your left side of your body will be the affected side. The same for the left side of your brain. Damage to the left affects the right side.
This is true even with something like vision. The left halves of each individual eye's visual field is processed by the right side of your occipital lobe, and the right by the left.
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