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The endpoint of both rays is the corner of Apple Avenue and Cherry Court.
Are north and east opposite directions?
North and south on Cherry Court or east and west on Apple Avenue.
No, see solution.
You both start your walk at the corner of Apple Avenue and Cherry Court. Therefore, the endpoint of both rays is at this corner.
You could also have walked along Apple Avenue, one going west and the other going east.
We know for sure that you and your friend walked in opposite directions. If you went east on Apple Avenue and your friend went north on Cherry Court, would you have walked in opposite directions?
East and north are not opposite directions. Knowing that you went in opposite directions, it is impossible that you went east on Apple Avenue and your friend went north on Cherry Court. Thus, your friend's claim is incorrect.