Derive the distance formula for points in the xy-plane.

What difficulties are you having with this?

This sounds like homework.
Can you show some of your thoughts on deriving this ?

I will give you some guidance.
Given that x and y axis are at right angles, you might want to apply Pythagoras' Theorem to the problem.

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We’re not here to do your homework for you. You need to show what you’ve done to try and answer the question