Modulus on both sides of an equation

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I've got a doubt while solving one of my problems on coordinate geometry. It's kinda conceptual doubt. I was just wondering what to do if I'm rendered with this situation:

| a - b | = | c - d |

The modulus comes from solving for areas of polygons in coordinate geometry. Say I've got variables on both sides, what do I do next?

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As the question is loose, so will the answer.

Rewrite as

$$(a_x-b_x)^2+(a_y-b_y)^2=(c_x-d_x)^2+(c_y-d_y)^2.$$